Name: 2hki Penn State Abington MATH 140 Calculus and Analytic Geometry I Mr. Ste

Question

Name: 2hki Penn State Abington MATH 140 Calculus and Analytic Geometry I Mr. Stephen Vallette Exam 4 Logarithmic and Exponential Functions Tuesday, December 16, 2014 For each multiple choice question, circle the letter or letters which best answer(s) each question. notation in each of the remaining responses. Show supporting work with clear statistical 1. Consider the function 2x+1 a. Give the domain, range, y-intercept ction (increasing/decreasing) of the function f() b. Find f (x). c. Compare and contrast the domain, range, y-intercept and direction of fu) with f'(x). (List their similarities and differences.)

Explanation / Answer

a)

f(x) = -3^(-2x + 1)

Domain : All real numbers
Range : (-infinity , 0)

y-intercept :

y = -3^(2(0) + 1)
y = -3^1
y = -3

Increasing everywhere

b)

f'(x) = -3^(-2x + 1) * ln(3) * (-2)

f'(x) = 3^(-2x + 1) * 2ln(3)

c)

Comparison :

Domain is the same for both f and f'
Range for f' is (0 , infinity) but range for f is (-infinity , 0)
y-intercept for f' is 6ln(3) but for f, it is -3
f'(x) is a function that DECREASES but f(x) is a function that INCREASES

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