Exercise 12 Page 659

Among the four given options, we are going to find the function with y-values that always increase as the corresponding x-values increase. To do this, let's draw the graphs of the functions once at a time.

Option F

We are given an absolute value function. y=|x|+2 Let's first make a table of values.

The table shows that as negative x-values increase, the corresponding y-values decrease, reaching its minimum value when x=0. As positive x-values increase, y-values also increase. Now, we will plot the points on a coordinate plane and draw the graph connecting them.

The graph confirms that y-values do not always increase as x-values increase.

Option G

We are given a quadratic function. y=x^2+2 Let's first make a table of values.

The table shows that as negative x-values increase, the corresponding y-values decrease, reaching its minimum value when x=0. As positive x-values increase, y-values also increase. Now, we will plot the points on a coordinate plane, and draw the a smooth curve connecting them.

The graph confirms that y-values do not always increase as x-values increase.

Option H

We are given a linear equation. y=x+2 Let's first make a table of values.

As we can see from the table, y-values always increase as the corresponding x-values increase. Let's also show this relation by plotting the points on a coordinate plane and connecting them with a line.

Therefore, the answer that we are looking for is option H.

Option I

We are given a linear function. y=- x-1 Let's first make a table of values.

The table shows that as x-values increase, the corresponding y-values decrease. Now, we will plot the points on a coordinate plane and draw a line connecting them.

The graph confirms that y-values do not increase as x-values increase. Our answer is confirmed to be option H.