PRE CALCULUS Functions

Question 1

What is the domain of f(x) = 1/(x-3)?

Accepted Answer

All real numbers except x = 3

Answer

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)?

Accepted Answer

19

Answer

(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?

Accepted Answer

A function that reverses the operation of the original function, where f(f⁻¹(x)) = x

Answer

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?

Accepted Answer

A test to determine if a graph represents a function — no vertical line should intersect the graph at more than one point

Answer

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?

Accepted Answer

y ≥ 0 (all non-negative real numbers)

Answer

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.

PRE CALCULUS Practice Test

PRE CALCULUS Practice Test

PRE CALCULUS Functions