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The graph of y= h (x) is shown. Draw the graph of y = - h (x) - 4

The graph of y= h (x) is shown. Draw the graph of y = - h (x) - 4-example-1
User Marylou
by
7.5k points

1 Answer

6 votes

Answer:

See graph

Explanation:

The transformation is as follows

The transformation of h(x) to -h(x) - 4 is a combination of two transformations

1. A reflection around the x -axis. Every point(x, y) in h(x) becomes (x', y') where x' = x and y' = -y so (x, y) → (x, -y)

2. A translation of each reflected point 4 units down; x value does not change but y values are shifted down so the new y is y'-4 = -y -4

The result of both transformations is:
every coordinate (x, y) in h(x) will be transformed to (x, -y -4)

Seeing as the graph consists of two straight lines meeting at the origin, all we need to do is take any 3 points in h(x), find the transformed coordinates and connect them with straight ilnes

h(x0 -h(X) - 4

(-2, 4) ⇒ (-2, -4-4) = (-2, -8)

(0, 0 ) ⇒ (0, -0 - 4) = (0, -4)

(4, 2) ⇒ (4, -2 -4) = (4, -6)

take these three points and plot

The graph of y= h (x) is shown. Draw the graph of y = - h (x) - 4-example-1
User Victorantunes
by
7.8k points

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