Unit 1 Test

Mth 163 Test-Unit I Name_______________________________

Sections 2.2, 3.1-3.5

1. Graph the following points on the graph and label each one: A(0,-2), B(-2,-1), and

C(4,-1).

2. Use your calculator to help you graph y=x 3 +x

2 – 2x.

3. Use your calculator to graph the following function and find the four intercepts.

Y = −1

36 𝑥3 +

5

36 𝑥2 +

1

2 𝑥 − 2

4.

If the graph above is a portion of a complete graph that is symmetric to the y-axis,

draw the other “half” of the graph.

5. Identify the equation whose graph is symmetric with respect to the x-axis.

[A] x=4y 2 -8 [B] y

2 =3x

4 -8 [C] 3x

2 =y [D] x=│y+4│

6. Draw a model of the relation {(-6,-8), (3,-3), (-6,-7), (9,7)}. Is the relation a

function? Why or why not?

7. Evaluate the function at the specified values of the independent variable and

simplify.

f(x) = 5

9 𝑥 + 9 Find f(-9) and f(27)

8. Evaluate the function at the specified values of the independent variable and

simplify.

f(x)={ −

1

2 𝑥 𝑖𝑓 𝑥 < 3

2 − 8𝑥 𝑖𝑓 𝑥 ≥ 3 }

[A] f(3) [B] f(0) [C] f(1) [D] f(3.9)

9. Find the domain of the function f(x) = √𝑥−10

𝑥2−6𝑥+8 .

10. A publishing company estimates that the average cost (in dollars) for one copy of a

new scenic calendar it plans to produce can be approximated by the function

C(x) = 4.75𝑥+475

𝑥 , where x is the number of calendars printed. Find the average cost per

calendar when the company prints 10,000 calendars.

11. Use the Vertical Line Test to determine if the graph below represents y as a

function of x

.

12. Use the graph of the function in #3 and determine the intervals on which it is

increasing, decreasing or constant.

13. Determine whether the function is even, odd, or neither.

f(x) = 5x 6 – 4x

2 – 9

14. Identify the common basic functions you have studied in section 3.2 that are

represented by the graphs in #4 and #11.

15. If f(x) =x 2 and h(x) = x

2 +2, how has the graph of f been transformed by h?

16. If f(x) = │x│, give the equation of the function that will shift the graph of this

equation 3 units to the right and 2 units upward,

17. Find (fg)(x) for f(x) =16 – x 2 and g(x) =4 – x.

18. If f(x) = x+5 and g(x) =√𝑥 + 5, find g(f(x)).

19. Sketch the graph of the function f(x) = [[x – 3]]. The symbol [[ ]] represents the

greatest integer function.

20. Find the inverse of the function f(x) = 𝑥−8

3 .