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Chapter 2: Q. 28 (page 69)

Determine whether the equation defines y as a function of $x$ .
$y = x^{3}$

Short Answer

Expert verified

The given equation is a function.

Step by step solution

01

Step 1. Given information

In the given question we have to determine whether the equation defines y as a function of x.

$y = x^{3}$

02

Step 2. The given equation is y=x3

The equation tells us to take an input $x$ and find their square.

For any input $x$ , these operations yield only one output $y$ .

03

Step 3. For example,

If $x = 1$ , then $y = {(1)}^{3} = 1$ .

If $x = 1$ , then $y = {(2)}^{3} = 8$ .

For this reason, the equation is a function.

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Most popular questions from this chapter

A rectangle is inscribed in a semicircle of radius $2$ . See the figure. Let $P = (x, y)$ be the point in quadrant I that is vertex of the rectangle and is on the circle.

Part (a): Express the area A of the rectangle as a function of x.

Part (b): Express the perimeter pof the rectangle as a function of x.

Part (c): Graph $A = A (x)$ . For what value of xis Alargest?

Part (d): Graph $p = p (x)$ . For what value of xis plargest?

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

$g (x) = \sqrt[3]{- x}$

Suppose that the x-intercepts of the graph of $y = f (x)$ are $- 5$ and $3$ .

(a) What are the x-intercepts of the graph of $y = f (x + 2)$ ?

(b) What are the x-intercepts of the graph of $y = f (x - 2)$ ?

(c) What are thex-intercepts of the graph of $y = 4 f (x)$ ?

(d) What are thex-intercepts of the graph of $y = f (- x)$ ?

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

$f (x) = x^{2} - 1$

True or False The domain of the function $f (x) = \frac{x^{2} - 4}{x}$ is ${x | x \neq \pm 2}$ .

See all solutions

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