Consider the graph of $$y = x^3$$ . Which statement is true about its domain and range?

Both the domain and range are $$x \geq 0$$ .

The domain is all real numbers, but the range is $$y \geq 0$$ .

The domain is $$x \geq 0$$ , but the range is all real numbers.

Given two functions $$f(x) = x^2$$ and $$g(x) = x + 2$$ , for which values of $$x$$ is $$f(x) > g(x)$$ ?

For all $$x$$ except between -2 and 2

If the function $$f(x) = \frac{1}{x}$$ , what is the range of $$f$$ ?

All real numbers except $$y = 0$$

All real numbers except $$x = 0$$

Which of the following represents the graph of a function with a decreasing rate of change?

A straight line with a positive slope.

A straight line with a negative slope.

What is the domain of the function $$f(x) = \frac{1}{(x - 2)(x + 3)}$$ ?

All real numbers except $$x = 2$$ and $$x = -3$$

If $$f(x) = x^2 - 4x + 4$$ and $$g(x) = -x^2 + 4x - 4$$ , which statement is true?

$$f(x)$$ opens upwards and $$g(x)$$ opens downwards.

$$f(x)$$ and $$g(x)$$ have the same vertex.

$$f(x)$$ and $$g(x)$$ intersect at two points.

$$f(x)$$ and $$g(x)$$ have no common points.

Which of the following is a correct interpretation of the graph of the function $$f(x) = x^3 - 3x^2 + 2x$$ ?

It has three distinct real roots.

It has two distinct real roots.

If $$f(x) = \sqrt{x}$$ and $$g(x) = \sqrt{x + 2}$$ , how does the graph of $$g$$ compare to the graph of $$f$$ ?

$$g$$ is shifted 2 units to the left.

$$g$$ is shifted 2 units to the right.

$$g$$ is compressed vertically.

What is the correct description of the end behavior of the function $$f(x) = -3x^5 + 2x^3 - x$$ ?

As $$x \rightarrow \infty$$ , $$f(x) \rightarrow -\infty$$ ; as $$x \rightarrow -\infty$$ , $$f(x) \rightarrow \infty$$ .

As $$x \rightarrow \infty$$ , $$f(x) \rightarrow \infty$$ ; as $$x \rightarrow -\infty$$ , $$f(x) \rightarrow -\infty$$ .

As $$x \rightarrow \infty$$ , $$f(x) \rightarrow 0$$ ; as $$x \rightarrow -\infty$$ , $$f(x) \rightarrow 0$$ .

As $$x \rightarrow \infty$$ , $$f(x) \rightarrow \infty$$ ; as $$x \rightarrow -\infty$$ , $$f(x) \rightarrow \infty$$ .

Which of the following is true for the function $$f(x) = \frac{x^2 - 4}{x - 2}$$ ?

It has a vertical asymptote at $$x = 2$$ .

It is continuous for all $$x$$ .

It has a horizontal asymptote at $$y = 2$$ .

Given the function $$f(x) = \frac{1}{(x + 1)^2}$$ , which statement is true about its graph?

It has a horizontal asymptote at $$y = 0$$ .

It has a vertical asymptote at $$x = -1$$ .

It has a vertical asymptote at $$x = 1$$ .

It has a horizontal asymptote at $$y = 1$$ .

For the function $$f(x) = |x + 3| - 2$$ , which of the following is true?

The graph is shifted 3 units to the left and 2 units down.

The vertex of the graph is at (-3, -2).

The graph is shifted 3 units to the right and 2 units down.

Functions Mastery Quiz

Authored by Carlo Damus

Mathematics

11th Grade

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The graph is shifted 3 units to the right.

The graph is shifted 3 units to the left.

The graph is stretched vertically.

The graph is compressed vertically.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Both have the same rate of change.

It cannot be determined from the given information.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Both the domain and range are all real numbers.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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