Question

Linear parent function fis graphed on the grid. 591 be . NE X B 2 al Which graph best represents h(x) = -f(x) + 3?

Answer 1

To answer this question, we need to identify the formula for the line equation in the graph.

We can see that if we take two points from the graph, we have:

(0, 0)

(1, 1)

Then, to find the equation for this line, we need to find the slope of the line first:

(0, 0) ---> x1 = 0, y1 = 0

(1, 1) ---> x2 = 1, y2 = 1

The slope is:

`m=(y_2-y_1)/(x_2-x_1)=(1-0)/(1-0)\Rightarrow m=1`

Applying the point-slope form of the line, we have:

`y-y_1=m(x-x_1)\Rightarrow y-0=1(x-0)\Rightarrow y=x`

Then, the function is y = x (as we can check from the graph).

Then, we have that:

`h(x)=-f(x)+3`

And

`f(x)=x\Rightarrow-f(x)=-x`

Therefore

`h(x)=-x+3`

Thus, we need to graph this line using the previous equation. We need to find the x-intercept for the line (the value of x when y = 0), and the y-intercept for the line (the value of y when x = 0). Then, we have:

`y=-x+3,y=0\Rightarrow0=-x+3\Rightarrow x=3`

Then, the x-intercept is (3, 0).

And the y-intercept is (x = 0):

`y=-(0)+3\Rightarrow y=3`

Hence, the y-intercept is (0, 3).

Therefore, if we put these two points on a graph (3, 0) and (0, 3), the graph will be:

We can see that the line has a different slope, and we can see that the y-intercept is 3, which corresponds with the new function.