Precalculus Functions, Domain and Range Quiz: 10 Questions with Explanations

A \((2,\infty)\)B \((-\infty,2]\)C \((-\infty,\infty)\)D \([2,\infty)\)

The radicand must be at least 0, so x – 2 >= 0 and x >= 2. The endpoint 2 gives f(2) = 0, so it is included.

A \(3\)B \(-3\)C \(15\)D \(-15\)

f(-3) = 9 + 2(-3) = 3. Forgetting that (-3) squared is positive gives a negative answer.

A \(6\)B \(0\)C \(-6\)D \(5\)

The denominator is 0 when x = -6. Many students exclude +6 by ignoring the sign.

A It is not a functionB It is a functionC It is a one-to-one functionD Its range is empty

Two points on one vertical line mean one input has two outputs, so the graph fails the vertical line test.

A \([0,\infty)\)B \((-\infty,3]\)C \([3,\infty)\)D \((-\infty,\infty)\)

Squares are at least 0, so f(x) is at least 3. Using 0 confuses the range with the x-squared part alone.

A \(3\)B \(2\)C \(5\)D \(4\)

Since 2 >= 2 the second rule applies, so f(2) = 4. Using x + 1 ignores the condition.

A \((1,\infty)\)B \([1,\infty)\)C \([0,\infty)\)D \((-\infty,1]\)

The graph starts at the closed point (1, 0) and goes right forever. That is [1, infinity).

A \((-\infty,4)\cup(4,\infty)\)B \((-\infty,4]\cup[4,\infty)\)C \((4,\infty)\)D \((-\infty,4)\)

All reals except 4 means two pieces that stop before 4 with parentheses.

A \([0,4]\)B \([-1,3]\)C \((-1,3)\)D \([-1,4]\)

The domain uses x-values from the left end (-1) to the right end (3). The interval [0, 4] is the range.

A \(3x\)B \(3\)C \(3h\)D \(3x+3h-5\)

f(x+h) – f(x) = 3h, and dividing by h leaves 3. The slope of a line is its constant rate of change.