Math 101 Exam 4 Questions And
Correct Answers 2025.
One-To-One - Answer A function is one-to-one if two inputs from the domain correspond to
different outputs in the range
- Each "y" in the range has one "x" from the domain
- Determine if it is one-to-one on a graph by horizontal line test (it only intersects the graph at
most in one-point)
- If one-to-one, an inverse function exists
How to Find the Inverse - Answer 1. check that f(x) is a function (one-to-one)
2. Replace x's with y's and y's with x's
3. Solve for y
4. Verify f○ f^-1 = x = f^-1○ f
How to Verify if f^-1 is the Inverse of f - Answer 1. f ○ f^-1 = f(f^1) = x
2. f^-1 ○ f = f^-1(f) = x
Exponential Function - Answer f(x) = ca^x
- c = initial value
- a = base
- x = growth factor
y = a^x, a > 1 - Answer - Graph is increasing
- Contains (0,1), (1,a), (-1,1/a)
- y-intercept is generally at (0,1)
- No x-intercept
- Horizontal a's at y = 0
- No vertical a's
y = a^x, 0 < a < 1 - Answer - Graph is decreasing
Correct Answers 2025.
One-To-One - Answer A function is one-to-one if two inputs from the domain correspond to
different outputs in the range
- Each "y" in the range has one "x" from the domain
- Determine if it is one-to-one on a graph by horizontal line test (it only intersects the graph at
most in one-point)
- If one-to-one, an inverse function exists
How to Find the Inverse - Answer 1. check that f(x) is a function (one-to-one)
2. Replace x's with y's and y's with x's
3. Solve for y
4. Verify f○ f^-1 = x = f^-1○ f
How to Verify if f^-1 is the Inverse of f - Answer 1. f ○ f^-1 = f(f^1) = x
2. f^-1 ○ f = f^-1(f) = x
Exponential Function - Answer f(x) = ca^x
- c = initial value
- a = base
- x = growth factor
y = a^x, a > 1 - Answer - Graph is increasing
- Contains (0,1), (1,a), (-1,1/a)
- y-intercept is generally at (0,1)
- No x-intercept
- Horizontal a's at y = 0
- No vertical a's
y = a^x, 0 < a < 1 - Answer - Graph is decreasing
