Questions: The graph of y=h(x) is shown. Draw the graph of y=h(2x)-4.

Transcript text: (b) The graph of $y=h(x)$ is shown. Draw the graph of $y=h(2 x)-4$.

Solution

Solution Steps

Step 1: Understand the Transformation

The given function is $ y = \frac{1}{3} h(2x) - 4 $. This involves three transformations:

Horizontal compression by a factor of 2.
Vertical scaling by a factor of $\frac{1}{3}$.
Vertical translation downward by 4 units.

Step 2: Apply Horizontal Compression

To apply the horizontal compression by a factor of 2, replace $ x $ with $ \frac{x}{2} $ in the function $ h(x) $. This means that every x-coordinate on the graph of $ h(x) $ will be halved.

Step 3: Apply Vertical Scaling

Next, apply the vertical scaling by multiplying the function by $\frac{1}{3}$. This means that every y-coordinate on the graph of $ h(x) $ will be scaled by $\frac{1}{3}$.

Step 4: Apply Vertical Translation

Finally, apply the vertical translation by subtracting 4 from the function. This means that every y-coordinate on the graph of $ h(x) $ will be shifted downward by 4 units.