Exercise 41 Page 259

Choose consecutive x-values to make a table of values in order to see the difference clearly.

See solution.

Practice makes perfect

We have been given the following function rules. y=2x and y=2x^2 We are asked to make a table of values and graph these functions in order to determine the change of the y-values when we double the x-values. Let's examine each function rule separately.

y=2x

Let's make a table of values for y=2x and graph it!

x	2x	y=2x	(x,y)
-1	2* (-1)	-2	( - 1, -2)
0	2* 0	0	( 0, 0)
1	2* 1	2	( 1, 2)
2	2* 2	4	( 2, 4)

Let's graph these points on a coordinate plane.

Now, let's double the x-values.

x	2x	y=2x	(x,y)
-2	2* (-2)	-4	( - 2, - 4)
0	2* 0	0	( 0, 0)
2	2* 2	4	( 2, 4)
4	2* 4	8	( 4, 8)

Let's graph our new values.

As we can see, when we double the x-values of y=2x, the y-values are also doubled but the graph remains the same.

y=2x^2

Now, let's apply the same process for y=2x^2.

x	2x^2	y=2x^2	(x,y)
-2	2*( -2)^2	8	( - 2, 8)
-1	2*( -1)^2	2	( - 1, 2)
0	2* 0^2	0	( 0, 0)
1	2* 1^2	2	( 1, 2)
2	2* 2^2	8	( 2, 8)

The corresponding graph for y=2x is the following.

Now let's see how the table changes when we double the x-values.

x	2x^2	y=2x^2	(x,y)
-4	2*( -4)^2	32	( - 4, 32)
-2	2*( -2)^2	8	( - 2, 8)
0	2* 0^2	0	( 0, 0)
2	2* 2^2	8	( 2, 8)
4	2* 4^2	32	( 4, 32)

Let's graph the new points.

In this case, when we double the x-values, the y-values quadruple but the graph again remains the same.

Subchapter links

Lesson Check p.257

Practice and Problem-Solving Exercises p.257-259

Standardized Test Prep p.259

Mixed Review p.259

Exercise 41 Page 259

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y=2x

y=2x^2