Name
Math 154 Practice Exam 2
Please work out each of the given
problems. Credit will be based on
the steps that you show towards the final answer.
Show your work.
Problem 1 Write as an exponential function
log7 x = y
Problem 3 Find the domain of
x2 - 5x - 1
x3 - 3x2 + 2x
Problem
4
A. All parabolas y = ax2 + bx + c are graphs of functions.
B. If the vertex of the parabola y = ax2 + bx + c has positive y-coordinate and the parabola is concave up, then the parabola has two x-intercepts.
C. If a graph of a function has two x-intercepts then the function is not 1-1.
Problem 5 Let f(x) = 3x + 2, g(x) = x + 3, and c(x) = -1. Find
A) f ° g (x)
B) f(x + h) - f(x)
h
C) g(f(1))
D) c ° f (2)
E)
c(x)g(x)
f(x) - 7c(x)
Problem 6 You are constructing a rectangular room such that one side of the room is 14 feet longer than the other side, and the distance from opposite corners is 26 feet. What are the dimensions of the room? Give your answer accurate to two decimal places.
Problem 7 Graph the quadratic function. Label any intercepts, the vertex, and the axis of symmetry.
y = -2x2 + 4x + 6
Problem 8 The
graphs of y = f(x) and y =
g(x) are given below. Find
A.
f(0)
B. g(-1)
C. g ° f (1)
D.
f(1)
g(-1)
Problem 9 Find the domain and range of the following functions
A. f(x) = 2x-1 + 3
B. f(x) = log8(x+2) - 4
Problem 10
Sketch the graph of y = 5x
.
Problem 11
Solve for w in
22w = 1/256
Problem 12
When a certain radioactive element decays, the amount to the element A at any time t is given by
A = 25 (2t/1500)
How much of the element will be left after 3000 years?
Problem 13
Sketch the graph of
y = -2(x - 1)2 + 5
Problem 14
If
f (x) = log3(2x - 1)
find
f -1(x)
Problem 15
The graph if the function y = f (x) is shown below. Determine if this function is 1-1.
