West Valley College Find the Linear Function Algebra Questions

Math 2 (Allen)Exam 1, part 2
name
2/16/22
To receive credit you must show your work. This exam is worth 150 points.
8) Use the graph to estimate the following (4 pts ea.)
a) the domain of f(x) is
range is
and the
b) the domain of (f + g) is
c) g(f(0)) =
y = f(x)
d) (g – f)(1) =
e) f is increasing on the interval(s)
y = g(x)
.
f) Sketch y = g -1(x)
f) Sketch y = g-1(x)
9) The function y = f(x) has a domain of [-8, ∞) and a range of (-∞, 10]. Find the domain and
range of: a) g(x) = f(x – 4) + 6
b) y = -f(2x)
c) y = f -1(x)
10) Given the graph of y = f(x) at the right,
sketch y = 2f(x – 1)
11) Find the linear function g(x) such that g(0) = 5 and g(6) = 53. Show your work.
For problems #12 – 19, let A(x) = x2 – 3x + 2, B(x) =
12) (3 pts ea.) The domain of B(x) is
√
and C(x) = 4x + 12
and the domain of C(x) is
13) B(0)
14) (A + C)(3)
15) A(A(-1))
16) B(C(1))
17) Is A(x) even, odd, or neither? No guesses – show your work.
18) (6 pts) Simplify A( x )  A(4)
x4
19) Find the average rate of change of A(x) on [0, 6]
20) Accurate to two decimals, find the intervals of inc/dec of f(x) = x 3 – 5x – 2
f is increasing on
and decreasing on
Solve the following equations.
21) 𝑥 + 1 = 5 + 𝑥
22) 8×2 – 23x – 3 = 0
23) 18x(4x – 3)2 + 12×2(4x – 3) = 0
24) |5 − 2𝑥| = |1 + 𝑥|
For the following inequalities, start by solving the corresponding equation (that is, pretend that
they are equations and solve). Plot the solutions on the number line, and then solve the inequality.
Write your answers using interval notation (6 pts ea.).
25) |2𝑥 + 1| > 9
25) |1 − 3𝑥| + 5 ≤ 10
26) (4 pts) The amount of trash, in tons, is modeled by T(x) = 32x + 180, where x = years since
2015. Identify and interpret the slope (write a brief sentence, and include units).
27) ACME car rental charges $30 per day plus $0.10 per mile, while UDrive’em car rental charges
$40 per day plus $0.05 per mile. How many miles would you have to drive so that the two
companies would charge the same amount. Don’t just guess and check – show the equations for
each company that models how they charge.
28) (5 pts) Given g(x) = √2𝑥 + 7, find g-1(x).
**** If you turned in P&P #1, you can skip this: On the gradesheet you will be identified by either
the last 4 digits of your student ID, or a 4-digit code of your choosing. I also randomize the grades
so they are not in alphabetical order. How shall I identify you? Please choose one:
a) use the last 4 digits of my ID
b) Use the following 4 digit code
After you upload your exam, close your browser, and then go back into Canvas and double
check that your file loaded.