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Exam (elaborations)

Math 4C UC San Diego – Fall 2024 Midterm 1 UCSD Practice Sample Exam

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2024/2025 Written for academic year
Institution University Of California - San Diego
Course MATH 4C
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This document is a practice exam for Math 4C at UC San Diego, created to prepare students for Midterm 1 in Fall 2024. It includes multiple-choice and short-answer problems covering key topics such as average rate of change, limits, function composition, inverses, quadratic transformations, secant lines, exponential functions, and applications of growth models. The exam also features applied problems like inflation modeling, making it closely aligned with the style and difficulty of the actual midterm.

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Q1
1 Point

Which of the following is the range of the function f (x) = x3 + 4 ?
(−∞, 4)
(4, ∞)
(−∞, ∞)
(−∞, 4]
[4, ∞)




Q2
1 Point

Let g(x) = 3x + 7. Find the average rate of change of g on the interval [2, 6].

3




Q3
1 Point

6x + 3
Find the limit of h(x) = as x → ∞.
3x − 5
​




2

, Q4
1 Point

f
Find the domain of if...
​




g
1. The domain of f is [4, 9), f (6) = 0, and f (x) > 0 for x =
 6. ​




2. The domain of g is [−1, 8], g(5) = 0, and g(x) > 0 for x =  5. ​




(−∞, ∞)
[−1, 9)
[4, 8]
[−1, 6) ∪ (6, 9)
[4, 5) ∪ (5, 8]
[−1, 5) ∪ (5, 6) ∪ (6, 9)
[4, 5) ∪ (5, 6) ∪ (6, 8]




Q5
1 Point

Let f (x) = x3 + 4. Find f −1 (3). If f is not invertible, write DNE instead of a
number.

-1

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