# Test #1 Review ```MATH 1314 – TEST #1 REVIEW – CHAPTER 2
1. Is { (2, 7), (3, 7), (5, 7) } a function?
2. Is {12, 13), (14, 15), (12, 19) } a function?
f(x) = 5 – 7x
3. Evaluate f(x) at each of the following and simplify:
a) f(4)
b) f(x + 3)
c) f(–x)
 x  4 if x  4
g(x) = 
 4  x if x  4
4. Evaluate g(x) at each of the following and simplify:
a) g(13)
b) g(0)
c) g(–3)
5. Use the vertical line test to determine if each graph is a function.
a)
b)
6. For each of the following graphs, state:
a) The domain
b) The range
c) x-intercepts (if any)
d) y-intercept (if any)
GRAPH A
e) intervals where f(x) is increasing
f) intervals where f(x) is decreasing
g) intervals where f(x) is constant
h) f(–2)
i) f(3)
GRAPH B
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7. Use Graph A (in problem #6) and list the relative maxima and relative minima.
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8. Determine if the following functions are even, odd, or neither. Use an algebraic test.
a) f(x) = x3 – 5x
b) f(x) = x4 – 2x2 + 1
9. Graph the following:
2 x if x  0
f ( x)  
 x if x  0
10. Find the difference quotient for f(x) = 8x – 11
11. Find the difference quotient for f(x) = –2x2 + x + 10
12. Find the slope of the line passing through the points (3, 2) and (5, 1).
13. Write the slope and y-intercept for each of the following lines:
a) y = 2/5 x – 1
b) f(x) = –4x + 5
14. Graph the following using x- and y-intercepts:
2x – 5y = 10
15. Use the graph of f(x) to graph each function g(x).
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a)
b)
c)
d)
g(x) = f(x + 2) + 3
g(x) = &frac12; f(x – 1)
g(x) = –f(2x)
g(x) = –f(–x) – 1
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16. Begin by graphing f(x) = x2, then graph each of the following:
a) g(x) = x2 + 2
b) g(x) = –(x + 1)2
17. Begin by graphing f(x) =
x , then graph g(x) =
x 3
18. Begin by graphing f(x) = x , then graph each of the following:
a) g(x) = x  2  3
b) g(x) =
1
2
x2
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19. Find the domain of each function. Write your answers in set-builder notation and interval notation.
a) f(x) = x2 + 6x – 3
4
b) g(x) =
x 7
c) h(x) = 8  2x
x
d) j(x) = 2
x  4 x  21
x 2
e) k(x) =
x 5
20. Find (f◦g)(x), (f◦g)(3), and (g◦f)(x):
a) f(x) = x2 + 3, g(x) = 4x – 1
b) f(x) = x , g(x) = x + 1
21. Find an equation for f –1(x) if f(x) = 4x – 3
22. Find an equation for f –1(x) if f(x) = 8x3 + 1
23. Find an equation for f –1(x) if f(x) =
2
x
5
24. Find the inverse function, then list the domain and range for f(x) and f –1(x)
a) f(x) = 1 – x2, x ≥ 0
b) f(x) = x  1
25. Use the horizontal line test to determine if each of the following graphs represent functions that
have inverses.
a)
b)
26. Graph the inverse of f(x) on the grid provided
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f(x)
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1. Yes
2. No
5.
a) –23
b) f(x + 3) = –16 – 7x
c) f(–x) = 5 + 7x
3.
4.
a) 3
b) 4
c) 7
a) Yes
b) No
6.
GRAPH A
a) [–3,5]
b) [–5,0]
c) (–3, 0) &amp; (5, 0)
d) (0, –2)
e) (–2,0)  (3,5)
f) (–3,–2)  (0,3)
g) none
h) –3
i) –5
7.
GRAPH B
a) [–∞,∞]
b) [–2,2]
c) (0, 0)
d) (0, 0)
e) (–2,2)
f) none
g) (–∞,–2)  (2,∞)
h) –2
i) 2
Relative min: (–2, –3) and (3, –5)
Relative max: (0, –2)
8.
a) Odd
b) Even
9.
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10. DQ = 8
13.
11. DQ = –4x – 2h + 1
a) m = 2/5, y-int = (0, –1)
b) m = –4, y-int = (0, 5)
14.
12. m = –&frac12;
y-int = (0, –2)
x-int = (5, 0)
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15. a) left 2, up 3
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b) vertical shrink of &frac12; , right 1
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c) horizontal shrink, reflect over x-axis
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d) reflect over x-axis, reflect over y-axis, down 1
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16. a) up 2
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b) reflect over x-axis, left 1
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17. left 3
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18.
a) left 2, down 3
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19.
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a)
(f◦g)(x) = 16x2 – 8x + 4
(f◦g)(3) = 124
(g◦f)(x) = 4x2 + 11
x 3
4
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22. f –1(x) =
(f◦g)(x) = x  1
(f◦g)(3) = 2
(g◦f)(x) = x  1
b)
3
x 1
8
3
or
x 1
2
Domain of f –1(x):  ,1
Range of f –1(x): 0, 
b) f –1(x) = (x – 1)2
Domain of f(x):
Domain of f –1(x):
0, 
1, 
a) Yes it has an inverse
b) No, it does not have an inverse
–1
Range of f (x):
2
x 5
23. f –1(x) =
a) f –1(x) = 1  x
Domain of f(x): 0, 
Range of f(x):  ,1
Range of f(x):
25.
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x |x isareal number  , 
x |x  7  ,7  7, 
x |x  4  ,4
x |x  7,3  , 7   7,3  3, 
x |x  2, but x  5 2,5   5, 
21. f –1(x) =
24.
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b) vertical shrink of &frac12;, right 2
1, 
0, 
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```