Pre-Calculus Review for Chapter 1
Name: _____________________________
1. Find the equation of the line that:
a. passes through the point (8, 5)
3
with a slope of m =
2
d. passes through the point (3, 6)
with a slope of 0.
b. passes through the point (-2, 3)
1
with a slope of m =
2
e. passes through the point (10, 5)
that is perpendicular to the line
3x + 5y = 5.
c. passes through the point (9, 2)
with an undefined slope.
f. passes through the point (-8, 3)
that is parallel to the line
-2x + 4y = 5.
2. During the 1st and 2nd years, a business had sales of $46,000 and $61,000 respectively. The
growth of sales follows a linear pattern. Use this information to find sales during the 3rd year.
3. For the function f(x)=
a. f(2)=
4. For the function h(x)=
a. h(0) =
6
, evaluate
2x  7
b. f(-3)=
c. f(1)=
d. f(-2)=
9  x , evaluate
b. h(9) =
c. h(5) =
d h(-7)=
5. Find the domain of the following functions:
7x 1
b. m(x)= 3x  9
a.g(x)=
2x  8
6. Given f(x) = 3 x + 5, simplify:
f ( x  m)  f ( x )
m
7. Given f(x) = 2 x 2 + 8 x – 15, simplify:
c. f(x)=
2x  2
x 2  25
d. h(x)=
m 0
f ( x  h)  f ( x )
h
h 0
8. Use the graph to identify the parent function, transformations, and write an equation.
parent function = ________________
.
transformations _________________
equation = ___________________
9. Use the graph to identify the parent function, transformations, and write an equation.
parent function = ________________
.
transformations _________________
equation = ___________________
9  3x
10. Identify the parent function, describe the transformations, and graph the function
a. f(x)= (x + 2)2 + 4
b. f(x)=
x 1  3
parent function =
parent function =
transformations =
transformations =
graph:
graph:
d. f(x)= | x  2 | 1
c. f(x)= (x – 1 3 + 2
parent function =
parent function =
transformations =
transformations =
graph:
graph:
11. Let f(x) = 4x – 5 and g(x) = 2x2 + 4, Find:
a. (f+g)(x) =
c. (f - g)(x)=
e. g(f(x) =
b. (fg)(x) =
d. f(g(x)) =
f. f(g(3))=
12. Show that f(x)= 3 – 5x and g(x)=
3 x
are inverses algebraically. (show that f(g(x)) and g(f(x)) = x
5
13. Find the inverse function algebraically for:
a. f(x) = 2x  5
b. f(x) =
x  16
c. f(x) = x 3  5
14. Use the graph to answer the questions:
a. Is it a function? _________
b. Does it have an inverse? _______
15. Use the graph to answer the questions:
a. Is it a function? _________
b. Does it have an inverse? _______
16. Use the graph to answer the following:
a. Identify the relative maximum: ________
b. Identify the relative minimum:_________
17. Evaluate f(x) =
a. f(3)
18. Identify:
2x + 8
x2 + 7
x<1
x>1
b. f(-2)
Domain ______________________
Range________________________
Where increasing _______________
Where decreasing _______________
19. Identify:
Domain ______________________
Range________________________
Where increasing _______________
Where decreasing _______________
20. Identify:
Domain ______________________
Range________________________
Where increasing _______________
Where decreasing _______________
c. f(1)