Plz ! what is the effect on the graph of the function f(x) = x when f(x) is replaced with −1/2f(x)? a) vertical reflection over x-axis and vertical stretch b) vertical reflection over x-axis and vertical compression c) horizontal reflection over y-axis and horizontal stretch d) horizontal reflection over y-axis and horizontal compression

Answer with explanation:

The given function is,

f(x)=x

We can Write it as,replacing f(x) by y

→y=x ------------------(1)

When , f(x) is replaced by in the above equation, the above equation reduces to

Similarly, Replacing f(x) by y in this equation also,the equation becomes

→→ y = - 2 x ---------------(2)

Plotting the graph of , Line 1 and Line 2

Now, when line 1 is reflected either through , x axis or y axis, the equation of line 1 becomes

→→y= -x

As,→ if there would have been vertical stretch, distance between origin and points on the curve would have been Larger.

But , →why compression because distance between axis of reflection and curve which has been compressed, that is , y=-2 x, has reduced.

Option D: Horizontal reflection over y-axis and horizontal compression

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).

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