1.
Given f(x) = -2x^{2} , evaluate f(-3).
Correct Answer
C. -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.
2.
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?
Correct Answer
B. Total monthly cost
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.
3.
This function is a graph of which of the following types of functions?
Correct Answer
E. 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.
4.
Describe the transformations from the parent function to h(x) = -2(x - 3)^{3} .^{ }
Correct Answer
D. Shift right, Stretch, then a Reflection across the x-axis
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.
5.
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?
Correct Answer
B. F(x) = -x + 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.
6.
Which of the following is the correct description for the end behavior of f(x) = -(x)^{2} + 3?
Correct Answer
B. 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.
7.
A set of functions with similar characteristics is the definition of . . .
Correct Answer
C. Family of Functions
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.
8.
True/False: The function f(x) = x^{3} has a maximum at (0, 0).
Correct Answer
B. False
Explanation
This function is a cubic function which creates a noodle shape. This function has no maximum (top) or minimum (bottom).
9.
Given the sequence 0, 1, 3, 6, 10, . . ., find S(7).
Correct Answer
A. 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.
10.
Using the table below, find the rate of change when x changes from -2 to 1.x -2 -1 0 1 2f(x) -6 1 2 3 10
Correct Answer
D. 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.
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.
Correct Answer
B. 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.
12.
Which of the following is the correct slope and y-intercept for the linear function f(x) = -5x + 8?
Correct Answer
A. Slope = -5, y-intercept = 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.