5
Math 95 – Exam 1 Practice Problem Solutions
1) Below is shown the graph of f(x)
a) Evaluate f(3)
2
b) Solve f(x) = 1
x = 0, 3.7
c) Find the average rate of the change from x =
1 to x = 5
(-1-2)/(5-1) = -3/4
4
3
2
1
0
-2
-1
-1 0
1
2
3
-2
2) Suppose the function A(t) gives the height of an airplane (in feet) t minutes after
takeoff. Explain the meaning of A(5) = 1000 in context of the situation.
After 5 minutes, the plane is 1000 feet height.
3) Given the function f(x) defined by the table below,
x
1
2
3
4
5
f(x)
2
4
5
6
5
6
3
7
-2
8
-1
a) Evaluate f(6)
3
b) Solve f(x) = 4
x=2
4) Suppose the following table shows the cost of a latte, in dollars, as a function of the
size of the latte, in ounces.
s
8
12
16
20
C(s)
2.0
2.5
3.0
3.5
a) Evaluate C(12) and give its meaning in practical terms
C(12) = 2.5. A cost of a 12 oz latte is $2.50
b) Solve C(s) = 3.0 and give its meaning in practical terms
s = 16. A 16 oz latte can be bought with $3
5) Circle all of the following that represent functions (marked with **)
in
out
1
2
4
5
6
6
4
1
**
**
in
out
2
3
3
5
5
6
4
5
in
out
**
2
5
4
7
6
6
7
4
**
4
5
6) a) Find a formula for the linear function graphed below.
find two points: (-1,4) and (2,3)
3 4
m=
= -1/3
2  (1)
y = -1/3x + b
3 = -1/3*2 + b <- plugging in (2,3)
3 = -2/3 + b
3+2/3 = b
b = 11/3 or about 3.67
6
5
4
3
2
1
0
-3
-2
-1 -1 0
1
2
3
4
5
y = -1/3x + 11/3
b) What is the domain and range of this function?
Domain: all real numbers (any number will work for x)
Range: all real numbers (can get any number out of the equation)
7) For a linear function y = f(t) with slope of 2 and y-intercept at –4, evaluate f(3)
f(t) = 2x - 4
f(3) = 2*3 - 4 = 2
8) Find the slope-intercept equation for a line passing through (1, -2) and (3,-3)
 3  (2)
m=
= -1/2
3 1
y = -1/2x + b
-2 = -1/2*1 + b <- plugging in (1,-2)
-2 = -1/2 + b
-2+1/2 = b
b = -3/2 = -1.5
y = -1/2x - 1.5
9) Match each graph with the corresponding line
a) y = 2x + 4
________A_________
b) y = 0.5x + 4
________F_________
c) y = 6
________D_________
d) x = 5
________E_________
e) y = -4 – 2x
________B_________
f) y = -4 – x
________C_________
F
B
D
C
E
A
10) Identify each phrase as relating to the slope or intercept of a line
a) … the population is growing by ….
b) … the initial height is …
c) … before we started production the cost was …
d) … she runs 5 miles per hour …
e) … at a temperature of zero …
f) … for each additional mile, he earned …
____slope________
____intercept____
____intercept____
____slope________
____intercept____
____slope________
11) A particular person has tracked the balance of her banking account (B) the last t days
since her paycheck. She has compiled the following data:
Balance ($)
280
250
190
160
Days since paycheck
2
3
5
6
a) Find a formula for B as a function of t.
m = (250-280)/(3-2) = -30/1 = -30
B= -30t+ b, so 280 = -30*2 + b, b = 340
B(t) = -30t + 340
b) What is the practical domain and range of this function
Answers may vary (especially upper limits)
Domain: reasonable values for t: 0 ≤ t ≤ 11
Range: reasonable values for B: 0 ≤ B ≤ 340
c) What will her balance be 10 days after her paycheck?
B(10) = -30*10 + 340 = $40
d) Explain the meaning of the slope of your formula in context of the problem
Her balance drops by $30 each day
e) Explain the meaning of the B intercept in context of the problem.
When she first got her paycheck, her balance was $340.
12) Two drugs are injected into a patient. The quantity of the first drug, A, still left in the
body after t minutes is given by A = 70 – 5t. The quantity of the second drug, B still
left in the body after t minutes is given by B = 50 – t. The patient requires a booster
shot when the quantity of drug B remaining is the same as the quantity of drug A.
When should the booster shot be given?
We want to solve for t when B = A, or
50-t = 70-5t
Add 5t to both sides
50 + 4t = 70
Subtract 50 from both sides
4t = 20
Divide by 4
t = 5 minutes
13) Jose went to the store to buy candy bars and soda. The candy bars cost $0.50 each,
the sodas were $1.25 each. He bought 10 items, and spent a total of $8 (before tax).
How many candy bars and sodas did he buy?
x: number of candy bars, y: number of sodas purchased
x + y = 10
0.50x + 1.25y = 8
(equation for number of items purchased)
(equation for costs)
Solution by substitution (not only way to solve)
1. Solve first equation for x
x = 10 - y
2. Substitute the expression “10 - y” in for x in the second equation
0.50(10 - y) + 1.25y = 8
3. Solve for y
5 - 0.50y + 1.25y = 8
5 + 0.75y = 8
0.75y = 3
y = 3/0.75 = 4
4. Go back and find x
x = 10 – y
x = 10 – 4 = 6
Jose bought 4 sodas and 6 candy bars.