Unit 1 Practice Test

1.

This function is a graph of which of the following types of functions?

Linear

Absolute Value

Quadratic

Cubic

Square Root

The graph of the function resembles the shape of a square root function. It starts at the origin and curves upwards, gradually becoming less steep. This is characteristic of a square root function, where the output value increases as the input value increases, but at a decreasing rate. Therefore, the correct answer is Square Root.

Explanation

The graph of the function resembles the shape of a square root function. It starts at the origin and curves upwards, gradually becoming less steep. This is characteristic of a square root function, where the output value increases as the input value increases, but at a decreasing rate. Therefore, the correct answer is Square Root.

2. Given the sequence 0, 1, 3, 6, 10, . . ., find S(7).

21

15

7

0

In this sequence a value has been added that is one value greater than the value added before. One was added, then two was added, then three, etc. To get the sixth term, five had to be added, which will give you 15. Then six had to be added to get the seventh term. 15 to 6 is 21.

Explanation

In this sequence a value has been added that is one value greater than the value added before. One was added, then two was added, then three, etc. To get the sixth term, five had to be added, which will give you 15. Then six had to be added to get the seventh term. 15 to 6 is 21.

3. Given f(x) = -2x² , evaluate f(-3).

18

36

-18

-36

You must plug -3 in for x. Order of operations tells you to complete exponents first. Therefore -3 squared is 9. Then you must multiply this by -2, which is -18.

Explanation

You must plug -3 in for x. Order of operations tells you to complete exponents first. Therefore -3 squared is 9. Then you must multiply this by -2, which is -18.

4. A set of functions with similar characteristics is the definition of . . .

Parent Function

Domain

Family of Functions

Range

Parent Function: The main function in a family of functions from which all other similar functions can be transformed.
Domain: All the possible input(x) values of a function.
Range: All the possible output(y) values of a function.

Explanation

Parent Function: The main function in a family of functions from which all other similar functions can be transformed.
Domain: All the possible input(x) values of a function.
Range: All the possible output(y) values of a function.

5. True/False: The function f(x) = x³ has a maximum at (0, 0).

True

False

This function is a cubic function which creates a noodle shape. This function has no maximum (top) or minimum (bottom).

Explanation

This function is a cubic function which creates a noodle shape. This function has no maximum (top) or minimum (bottom).

6. Which of the functions below is the correct function for the parent linear function that has been reflected across the y-axis and shifted up 5?

F(x) = x + 5

F(x) = -x + 5

F(x) = -x - 5

F(x) = x -5

This graph is a linear function because it forms a line. However, this function represents the parent linear function that has been reflected across the y-axis and then shifted up 5.

Explanation

This graph is a linear function because it forms a line. However, this function represents the parent linear function that has been reflected across the y-axis and then shifted up 5.

7. Which of the following is the correct slope and y-intercept for the linear function f(x) = -5x + 8?

Slope = -5, y-intercept = 8

Slope = 8, y-intercept = -5

Slope = 5, y-intercept = 8

Slope = -8, y-intercept = 5

Slope-intercept form: y=mx+b, where m is your slope and b is your y-intercept. You are given f(x)=-5x + 8 which is the same thing as y=-5x+8. Therefore m or your slope is -5 and b or the y-intercept is 8.

Explanation

Slope-intercept form: y=mx+b, where m is your slope and b is your y-intercept. You are given f(x)=-5x + 8 which is the same thing as y=-5x+8. Therefore m or your slope is -5 and b or the y-intercept is 8.

8. The function c(m) = .25m + 10, represents the total monthly cost for a cell phone, where m represents the number of minutes used. What is the dependent quantity?

Number of Minutes

Total monthly cost

Cost per minute

Y or f(x) is always your dependent variable. Also, the dependent variable depends on the x or the independent variable. In this case the total monthly cost depends on the number of minutes used that month.

Explanation

Y or f(x) is always your dependent variable. Also, the dependent variable depends on the x or the independent variable. In this case the total monthly cost depends on the number of minutes used that month.

9. Which of the following is the correct description for the end behavior of f(x) = -(x)² + 3?

Both arms reach up

Both arms reach down

Right arm reaches up, Left arm reaches down

Right arm reaches down, Left arm reaches up

One arm reaches right

This function is a quadratic function which means it forms a U. However, it has been reflected across the x-axis so it is facing down. Therefore, both arms reach down.

Explanation

This function is a quadratic function which means it forms a U. However, it has been reflected across the x-axis so it is facing down. Therefore, both arms reach down.

10. Using the table below, find the rate of change when x changes from -2 to 1.

x -2 -1 0 1 2
f(x) -6 1 2 3 10

-3

1/3

-1/3

3

Rate of Change is found by finding the difference of the outputs(y) and dividing by the difference of the inputs(x). The input values are given here. x= -2 and x =1. You must find the output values that correspond. -6 corresponds to -2 and 3 corresponds to 1. The difference of the output is (-6-3)=-9. The difference of the input is (-2-1)=-3. This gives us -9/-3, which is 3.

Explanation

Rate of Change is found by finding the difference of the outputs(y) and dividing by the difference of the inputs(x). The input values are given here. x= -2 and x =1. You must find the output values that correspond. -6 corresponds to -2 and 3 corresponds to 1. The difference of the output is (-6-3)=-9. The difference of the input is (-2-1)=-3. This gives us -9/-3, which is 3.

11. Describe the transformations from the parent function to h(x) = -2(x - 3)³ .

Shift down, Stretch, then a Reflection across the y-axis

Shift right, Shrink, then a Reflection across the x-axis

Shift left, Shrink, then a Reflection across the y-axis

Shift right, Stretch, then a Reflection across the x-axis

When a number has been subtracted from the value of x, this causes a horizontal shift right. Hence the - 3 causes the function to shift right.
When a function is multiplied by a value greater than one, the function stretches. Hence, the 2 causes the function to stretch.
When a function is negative it causes the function to reflect across the x-axis. Hence the - causes this function to reflect.

Explanation

When a number has been subtracted from the value of x, this causes a horizontal shift right. Hence the - 3 causes the function to shift right.
When a function is multiplied by a value greater than one, the function stretches. Hence, the 2 causes the function to stretch.
When a function is negative it causes the function to reflect across the x-axis. Hence the - causes this function to reflect.

12. The function g(x) = 10x represents the total profit from selling t-shirts, where x is the number of t-shirts sold. Find the rate of change when the number of t-shirts increases from 3 to 10.

7

10

70

5

You are given x=3 and x=10. To find the corresponding output values, you must plug 3 and 10 into the function. When you evaluate g(3) you get 30 and when you evaluate g(10) you get 100. Therefore the difference of the output is (100-30)=70 and the difference of the input is (10-3)=7. Therefore you get 70/7, which is 10.

Explanation

You are given x=3 and x=10. To find the corresponding output values, you must plug 3 and 10 into the function. When you evaluate g(3) you get 30 and when you evaluate g(10) you get 100. Therefore the difference of the output is (100-30)=70 and the difference of the input is (10-3)=7. Therefore you get 70/7, which is 10.