   Chapter 2, Problem 5RE

Chapter
Section
Textbook Problem

Let y2 = 2x + 1. a. Sketch the graph of this equation. b. Is y a function of x? Why? c. Is x a function of y? Why?

(a)

To determine

To sketch: The graph of the given function.

Explanation

The given function is,

y2=2x+1 (1)

Graph:

Substitute the values of x to find the value of the function.

Substitute 0 for x in equation (1) to find the value of y ,

y2=20+1y2=0+1y2=1y2=1(Takesquarerootofbothsides)

Further solve the above equation,

y2=1y=±1(y2=yand1=1)

Substitute 0.5 for x in equation (1) to find the value of y ,

y2=2(0.5)+1y2=1+1y2=0y2=0(Takesquarerootofbothsides)

Further solve the above equation,

y2=0y=0(y2=yand0=0)

Substitute 1 for x in equation (1) to find the value of y ,

y2=21+1y2=2+1y2=3y2=3(Takesquarerootofbothsides)

Further solve the above equation,

y2=3y=3(y2=yand3=3)

Substitute 2 for x in equation (1) to find the value of y ,

y2=22+1y2=4+1y2=5y2=5

(b)

To determine

To explain: Whether y is a function of x with explanation.

(c)

To determine

To explain: Whether x is a function of y with explanation.

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