PRE CALCULUS Functions — Questions and Answers
Question 1: What is the domain of f(x) = 1/(x-3)?
- All real numbers
- All real numbers except x = 3 (Correct answer)
- x > 3 only
- x < 3 only
Correct answer: All real numbers except x = 3
The function is undefined when the denominator equals zero. Setting x-3 = 0 gives x = 3, so the domain excludes x = 3.
Question 2: If f(x) = 2x + 1 and g(x) = x², what is (f ∘ g)(3)?
- 19 (Correct answer)
- 49
- 10
- 7
Correct answer: 19
(f ∘ g)(3) = f(g(3)) = f(9) = 2(9) + 1 = 19. First evaluate the inner function, then apply the outer function.
Question 3: What is an inverse function?
- The negative of a function
- A function that reverses the operation of the original function, where f(f⁻¹(x)) = x (Correct answer)
- A function multiplied by -1
- A function with no solutions
Correct answer: A function that reverses the operation of the original function, where f(f⁻¹(x)) = x
An inverse function 'undoes' the original function. If f(2) = 5, then f⁻¹(5) = 2. The functions reverse each other's operations.
Question 4: What is the vertical line test?
- Testing if a line is perfectly vertical
- A test to determine if a graph represents a function — no vertical line should intersect the graph at more than one point (Correct answer)
- Testing the y-axis
- A test for parallel lines
Correct answer: A test to determine if a graph represents a function — no vertical line should intersect the graph at more than one point
If any vertical line crosses the graph at more than one point, the graph fails the test because that x-value would have multiple y-values, violating the definition of a function.
Question 5: What is the range of f(x) = x²?
- All real numbers
- y ≥ 0 (all non-negative real numbers) (Correct answer)
- y > 0 only
- y ≤ 0 only
Correct answer: y ≥ 0 (all non-negative real numbers)
Since squaring any real number produces a non-negative result, the range of f(x) = x² is all values greater than or equal to zero.
Question 6: What is a piecewise function?
- A function that is broken
- A function defined by different expressions for different intervals of the domain (Correct answer)
- A function with multiple y-intercepts
- A function that can only be graphed in pieces
Correct answer: A function defined by different expressions for different intervals of the domain
Piecewise functions use different formulas for different parts of their domain. For example, |x| is defined as x when x ≥ 0 and -x when x < 0.
PRE CALCULUS Functions
What is the domain of f(x) = 1/(x-3)?