Grima MAT 151
Chapter 3 Practice test
#1 –2: Determine the domain and range of each function, write your answer in interval notation when
appropriate.
1)
2)
y
4
3
(5,2)
2
(-3,1)
(2,1)
1
(0,0) (3,0)
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
x
5
6
7
8
9
10
11
-1
-2
-3
-4
#3-5: Use algebra to find the domain of each function. Write your answer in interval notation, or in
words.
3) 𝑓(𝑥) =
𝑥−4
𝑥 2 +3𝑥+2
5) f(x) = x2 – 16
4) 𝑓(𝑥) = √𝑥 − 6
#6 – 8: let f(x) = x2 + 2x + 5 and g(x) = 3x – 1, find the following
6) (f-g)(x)
7) (𝑔 ∘ 𝑓)(𝑥)
8) (f+g)(2)
9) Find the difference quotient; that is find
𝑓(𝑥+ℎ)−𝑓(𝑥)
;
ℎ
f(x) = 2x – 3
10) Find the average rate of change of f(x) = x3 + 6x2 from 0 to 2
#11-13 describe how the graph of the given function relates to the graph of a common function
11) f(x) = (x-2)2 + 4
12) f(x) = −√𝑥 + 3 + 5
13) 𝑓(𝑥) = |𝑥 + 3| − 4
14) Write the function whose graph has the same shape as the graph of f(x) = x2 but is shifted to the
right 3 units and up 2 units.
Use the graph below to answer #10 – 15, call the function graphed below h(x)
15) find the x-intercepts
17) for what values of x is h(x) = 4
19) what is the domain of h
16) find the y-intercept
18) find h(4)
20) what is the range of h
Use the graph below to answer questions 21 – 26.
(You should also be able to find the domain and range of this graph)
21) the interval(s) where the function graphed is increasing
22) the interval(s) where the function graphed is decreasing
23) The values of x (if any) where the function has a local maximum
24) The local maximum value (if any)
25) The values of x (if any) where the function has a local minimum
26) The local minimum values (if any)
27) A campground owner has 1000 meters of fencing. He wants to enclose a rectangular field bordering
a river, with no fencing needed along the river. Let W represent the width of the field. Follow these
steps to find the dimensions of the field that yields the largest area.
a) Write an expression for the length of the field
b) Write an equation for the area of the field.
c) Find the value of w leading to the maximum area
d) Find the value of L leading to the maximum area
e) Find the maximum area
Answers:
1) Domain [3, ∞) Range (−∞, 0] 2) Domain {-3,0,2,3,5} Range {0,1,2}
3) Domain: All real numbers except -1, -2
4) Domain [6, ∞) 5) Domain all real numbers
6) x2 – x + 6 7) 3x2 + 6x + 14 8) 18 9) 2
10) 16 11) shifted right 2 up 4 12) reflected over x-axis, shifted left 3 up 5
13) left 3 down 4
14) g(x) = (x-3)2 + 2
15) (-1,0) (3,0) 16) (0,3) 17) x = 1 18) -5 19) (−∞, ∞) 20) (−∞, 4]
21) (−∞, −1) ∪ (1, ∞) 22) (-1, 1)
23) x = -1 24) max y-value y = 4
25) x = 1 26) min y-value y = 0
27 was missed by many last semester and will likely be on your test
27a) L = 1000 – 2W
27b) A = LW or A = (1000 – 2W)W or A = 1000W – 2W2
27c) W = 250 FT
27d) L = 500 FT
27e) 125000 square feet
Extra word problem for practice
28) A campground owner has 500 meters of fencing. He wants to enclose a rectangular field bordering
a river, with no fencing needed along the river. Let W represent the width of the field. Follow these
steps to find the dimensions of the field that yields the largest area.
a) Write an expression for the length of the field
b) Write an equation for the area of the field.
c) Find the value of w leading to the maximum area
d) Find the value of L leading to the maximum area
e) Find the maximum area