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Chapter 3: Q 3.94 (page 320)

Determine whether each equation is a function.

  1. x+y2=4
  2. y=x2-7
  3. y=5x-4

Short Answer

Expert verified

Part (a) x+y2=4is not a function.

Part (b) y=x2-7is a function.

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

Step by step solution

01

Part (a) Step 1.

The equation is:

x+y2=4

The above equation can be written as:

y2=4-x

Substitute x=0in the above equation,

y2=4-0=4y=2or-2

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.

02

Part (b) Step 1.

The equation is:

y=x2-7

Substitute x=0in the above equation,

y=02-7=0-7=-7

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.

03

Part (c) Step 1.

The equation is:

y=5x-4

Substitute x=0in the above equation,

y=50-4=0-4=-4

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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Most popular questions from this chapter

Graph the equation by plotting points .

y=-2x+4

Find the equation of a line with slope -1and y-intercept(0,-3).

Find the intercepts of the graph

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In the following exercises, find the equation of a line containing the given points. Write the equation in slope鈥搃ntercept form.

(7, 1) and (5, 0)

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Slope-34and y-intercept0,-2.
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