Name:_______________________________________
Algebra 1
Practice for Test #1 –Solving, Functions, Slope, Average Rate of Change
And Everything Else
1. Use the functions below to calculate the value each expression.
f(x) = 3x2 – 5
g(x) = -4x + 1
1.b.) −4 ∙ 𝑓(−3) + 2 ∙ 𝑔(4)
1.a.) f(-2)
2. Find the x and y intercepts of the functions below.
y = 3x – 5
1
f(x) = 2 𝑥 + 4
3x – 5y = 9
3. Examine the graph of f(x) and g(x) below. Use it to answer the questions.
𝒈(𝒙)
𝒇(𝒙)
Find each of the following:
a.) f(-9)
b.) g(-5)
e.) Find a so that f(a) = -5
c.) −2 ∙ 𝑓(1)
d.) 𝑓(5) − 𝑔(6)
f.) What is the input value, such that the output of g(x) is 10.
g.) Find a and b so that f (a)  f (b).
h.) Explain how you know that the graph of f(x) represents a function, using the vertical line test.
i.) Label the domain and range of g(x).
4. Chris’s parents are having a birthday party for his sister and want to have a magician perform at the party.
Magician # 1 charges a $40 set-up fee and then $30 per hour. Magician # 2 charges $20 per hour and an $80
set-up fee.
a) Write a separate equation C(t) for each magician that represents each magician’s charges C (in dollars) in
terms of time t (measured in in hours).
b) Write another equation and solve it to find out how many hours will these magicians have to work in order
for their total costs to be the same.
c) What is the cost of the magician when both magicians have the same cost?
6. Solve each equation.
 8x  4(5  3x)  1  6 x  19  10 x
3
2
(4  2 x)  (8  4 x)  3
5
3
8x  3 5x  4

2
6
−6
7
𝑥 = −11
7.a. Draw a graph below that passes the vertical line test. Explain.
7.b. Draw a graph below that does NOT pass the vertical line test. Explain.
7.c. Explain what the vertical line test is and explain how it works.
8. Label the domain and range of each linear function below.
Domain: _________________
Domain: _________________
Domain: _________________
Range: ___________________
Range: ___________________
Range: ___________________
Domain: _________________
Domain: _________________
Domain: _________________
Range: ___________________
Range: ___________________
Range: ___________________
9. Solve the inequality below, and
graph the solutions on a number line.
10. Find the missing coordinate.
(3, y) and (5, 8)
14 – 4x < 46
m=3
11. Solve each equation below.
-3(2x – 4) = -6x + 12
4x – 6 = 10x – 4 – 6x – 6
12. As a scuba diver descends into deeper water, the pressure of the water on the diver’s body steadily
increases. The pressure at the surface of the water is 2117 pounds per square foot. The pressure increases at a
rate of 64 pounds per square foot for each foot the diver descends.
12.a.) Write a function P(d) which denotes the amount of pressure P on the diver’s body (measured in pounds
per square foot) with respect to the diver’s depth underwater d (measured in feet).
12.b.) Find P(10). Explain what it represents.
12.c.) Find d, such that P(d) = 3397.
Explain what it represents.
13. Find the slope of the line that passes through the points (-4, 6) and (8, -3), and describe the line.
14. Find the slope of the line that passes through the points (-3, 5) and (-7, 5), and describe the line.
15. Find the slope of the line that has an x-intercept of 6 and a y-intercept of -3, and describe the line.
16. The graph below describes the temperature in a Caribbean City (measured in degrees Celsius) as a function
of the time (measured in hours since noon) on a given day.
Complete the following sentence.
Between 3:30pm and 8:30pm, the temperature decreased, on average,
by approximately _______________ degrees Celsius each hour.