Chapter 3: Q 3.94 (page 320)

Determine whether each equation is a function.
$x + y^{2} = 4$
$y = x^{2} - 7$
$y = 5 x - 4$

Short Answer

Expert verified

Part (a) $x + y^{2} = 4$ is not a function.

Part (b) $y = x^{2} - 7$ is a function.

Part (c) $y = 5 x - 4$ is a function.

Step by step solution

Part (a) Step 1.

The equation is:

x + y^{2} = 4

The above equation can be written as:

$y^{2} = 4 - x$

Substitute $x = 0$ in the above equation,

$\begin{array}{rcl} y^{2} & = & 4 - 0 \\ = & 4 \\ y & = & 2 o r - 2 \end{array}$

It would work similarly for any value of x. Since each value of x does not correspond to only one value of y the equation does not define a function.

Part (b) Step 1.

The equation is:

$y = x^{2} - 7$

Substitute $x = 0$ in the above equation,

$\begin{array}{rcl} y & = & {(0)}^{2} - 7 \\ = & 0 - 7 \\ = & - 7 \end{array}$

It would work similarly for any value of x. Since each value of x corresponds to only one value of y the equation defines a function.

Part (c) Step 1.

The equation is:

$y = 5 x - 4$

Substitute $x = 0$ in the above equation,

$\begin{array}{rcl} y & = & 5 (0) - 4 \\ = & 0 - 4 \\ = & - 4 \end{array}$

It would work similarly for any value of x. Since each value of x corresponds to only one value of y the equation defines a function.

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Determine whether each equation is a function.
$x + y^{2} = 4$
$y = x^{2} - 7$
$y = 5 x - 4$

Short Answer

Step by step solution

Part (a) Step 1.

Part (b) Step 1.

Part (c) Step 1.

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Determine whether each equation is a function.x+y2=4y=x2-7y=5x-4

Short Answer

Step by step solution

Part (a) Step 1.

Part (b) Step 1.

Part (c) Step 1.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Determine whether each equation is a function.
$x + y^{2} = 4$
$y = x^{2} - 7$
$y = 5 x - 4$