Title: M2.5 Functions Quiz
Course: Technical Math for Industry > Section: Module 2.5 Math Functions

Q: Which of the relations given by the following sets of ordered pairs is not a function?
A: (a choice with no text)
Feedback: Correct. The input 3 has two outputs: 2 and 5. Therefore, the relation is not a function.
Feedback: Incorrect. You may have thought this relation was not a function because the output 2 is the same for every input. However, each input has only one output, so this relation is a function.
Feedback: Incorrect. You may have thought this relation was not a function because the output occurs more than once. However, each input has only one output, so this relation is a function.
Feedback: Incorrect. You may have thought this relation was not a function because the input and output values are all negative. However, each input has only one output, so this relation is a function.

Q: Which function has the following domain and range?

Domain:

Range:
A: (a choice with no text)
Feedback: Incorrect. You may have chosen this function because the ordered pairs show the least and greatest values from the domain and the range. However, the domain is the set of all input values, and this set of input values does not match the domain given in the problem. Also, the range is the set of all output values, and this set of output values does not match the given range in the problem.
Feedback: Incorrect. You may have mixed up the definition of the domain and range of a function. The domain is the set of all input values, or x-coordinates, and the range is the set of all output values, or y-coordinates. The set of input values does not match the domain given in the problem, and the set of output values does not match the range given in the problem.
Feedback: Incorrect. You may have looked at only the first few ordered pairs in this function. The set of input values does not match the given domain, and the set of output values does not match the given range.
Feedback: Correct. Organize the ordered pairs in a table. The set of input values matches the domain given in the problem: . The set of output values matches the range given in the problem: . Some of the ordered pairs may have the same y-coordinate, but they only need to be listed once in the set.

Q: Which graph represents a function?
A: (a choice with no text)
Feedback: Correct. Draw a vertical line through each point on the graph. Because no line intersects any other point, the graph represents a function.
Feedback: Incorrect. If you draw the vertical line , you will find that it passes through two points. Therefore, the graph fails the vertical line test and does not represent a function.
Feedback: Incorrect. If you draw the vertical line , you will find that it passes through two points. Therefore, the graph fails the vertical line test and does not represent a function.
Feedback: Incorrect. You may have done a horizontal line test instead of a vertical line test. If you draw a vertical line through any point on the graph with or , you will find that the line passes through more than one point. Therefore, the graph fails the vertical line test and does not represent a function.

Q: Given , find .
A: (a choice with no text)
Feedback: Correct. Substitute the expression into the function for x: Use the distributive property on the right side: Combine like terms to simplify:
Feedback: Incorrect. You substituted the expression for the entire term , instead of just for x. Your first step should be to replace x by : . Then simplify this expression.
Feedback: Incorrect. You may have correctly substituted for x to get , but you did not simplify correctly. You should first use the distributive property and then combine like terms.
Feedback: Incorrect. You multiplied the expression in the function by , instead of substituting for x. Your first step should be to replace x by : . Then simplify this expression.

Q: Which of the following is the graph of ?
A: (a choice with no text)
Feedback: Incorrect. When evaluating for negative inputs, you may have forgotten that a negative times a positive is negative. is a linear function; its graph is a straight line.
Feedback: Incorrect. When creating a table of values for the function, you may not have taken into account the addition of the constant 1. This graph matches the function , not .
Feedback: Incorrect. You may have chosen this graph because it crosses the x-axis at 3 and the y-axis at 1, which are numbers you recognize from the function. Instead, you should create a table of values for the function, evaluating the function for different inputs and finding the related outputs.
Feedback: Correct. Make a table of values with inputs , 0, and 1, for example. Evaluate the function for each value of x, and record the output, . Each row in your table forms an ordered pair. These points would be , , and . The graph contains these points and is a straight line.

Q: Which of the functions is represented by the graph?
A: (a choice with no text)
Feedback: Incorrect. You probably recognized that the graph is a parabola that opens down, so you chose a quadratic function with the correct vertex, . However, the graph of also contains the points and , for example, and these are not on the given graph.
Feedback: Correct. Make a table of values and evaluate different inputs for the function. Each row in the table is an ordered pair, which gives you a point on the graph. Some of these are , , , , and . These points are all on the graph.
Feedback: Incorrect. You may not have noticed that this answer is a linear function, so its graph would be a line. The given graph is a parabola, which is the graph of a quadratic function, or one in the form .
Feedback: Incorrect. You may not have noticed that the coefficient of this quadratic function is positive, although it has the same vertex as in the graph (0, 4). The graph of would open up because of the coefficient , not down like the given graph.

Q: Which of the following is a graph of ?
A: (a choice with no text)
Feedback: Incorrect. You confused the graph of with the graph of (shown in this answer). When you multiply the radical by a negative number, the direction of the graph changes, because the function decreases as x increases. So the real graph is going down.
Feedback: Incorrect. This is a graph of . When you multiply the radical by a negative number, the direction of the graph changes, because the function decreases as x increases.
Feedback: Incorrect. This is a graph of . When you subtract a number outside the radical, the graph moves down. When you add a number outside the radical, the graph moves up.
Feedback: Correct. Multiplying the radical by a negative number changes the direction of the graph. Adding 3 outside the radical means the graph will move three up. The graph of will begin at and decrease, as does this graph. Check further by evaluating the function for different inputs. The graph must pass through , , and , and it does.

Q: Find the domain of .
- all real numbers (Incorrect. You may have thought that because the variable in the radical is squared, the domain includes all real numbers. However, the domain is restricted to all x-values for which the radicand is not negative. That is, . The domain is the solution of this inequality.)
- or (Correct. The value under the radical in a square root function cannot be less than 0. So the domain is all x-values for which the radicand is not negative. That means , so . This inequality is true only when x is greater than or equal to 6, or x is less than or equal to : or .)
A: or
Feedback: Incorrect. You may have correctly set up the inequality , but when solving the inequality, you forgot to include negative values that would also make the inequality true.
Feedback: Incorrect. You may not have noticed the exponent in the expression in the radicand. Because the domain is restricted to all x-values for which the radicand is not negative, you need to solve for the inequality . Include both negative and positive values that would make the inequality true.

Q: What are the domain and range of the real-valued function ?
- The domain is , and the range is all real numbers. (Incorrect. You correctly identified the domain of the function. However, you may not have graphed the function to find the range. Because the square root symbol cannot have a negative value, . Use this fact to find the range.)
- The domain is , and the range is . (Incorrect. You correctly identified the range of the function. The domain is all the x-values for which the radicand is not negative. This means that . Use this to find the domain.)
- The domain is , and the range is . (Correct. The domain of a radical function is all the x-values for which the radicand is not negative. That means , so the domain is . By definition, the square root symbol cannot have a negative value, so . That means . Therefore, the range is .)
- The domain is , and the range is . (Incorrect. You correctly identified the domain of the function. However, you may not have graphed the function to find the range. Because the square root symbol cannot have a negative value, . Use this fact to find the range.)
A: The domain is , and the range is .

Q: Find .
A: (a choice with no text)
Feedback: Incorrect. You may have thought that the notation meant that you had to do some multiplication, but it does not. The notation should be interpreted as follows: Then rearrange and combine like terms.
Feedback: Correct.
Feedback: Incorrect. You may have tried to combine like terms, but you made a mistake with a sign.
Feedback: Incorrect. It appears that while combining like terms, you also added the exponents. Remember that when you combine like terms, you need only add the coefficients; the variable factor remains the same.

Q: Find .
A: (a choice with no text)
Feedback: Incorrect. It appears that you have made some sign errors when subtracting. Start with: Be sure to distribute the minus sign to all terms of the second function and then combine like terms.
Feedback: Incorrect. Be careful to subtract in the correct order. Start with: Distribute the minus sign to all terms of the second function and then combine like terms.
Feedback: Incorrect. It appears that you added the two functions instead of subtracting them. Start with: Be sure to distribute the minus sign to all terms of the second function and then combine like terms.
Feedback: Correct.

Q: Find .
A: (a choice with no text)
Feedback: Correct.
Feedback: Incorrect. It appears that you multiplied exponents while finding the product of the two functions. When multiplying terms with the same base, multiply the coefficients and add the exponents. Start with: Use the distributive property.
Feedback: Incorrect. You may have thought that the notation meant that you should multiply the product of f and g by x, but it does not. The correct interpretation of this notation is: Use the distributive property.
Feedback: Incorrect. It appears that you did not distribute the factor to all terms in the second function. Start with: Use the distributive property.

Q: Find:
- 8 (Incorrect. You may have found: The correct setup for the problem is: Factor the numerator and simplify.)
- 4 (Correct.)
A: 4
Feedback: Incorrect. It appears that you subtracted instead of dividing. The correct setup for the problem is: Factor the numerator and simplify.
Feedback: Incorrect. You may have just divided the coefficients and the constants. The correct setup for the problem is: Factor the numerator and simplify.