Consider the same transformation ℎ ( 𝑥 )

To transform the point $(-1, 0)$ using the given transformation $h(x) = f(2x - 3)$, follow these steps:

1. Start with the point: $(-1, 0)$. The first coordinate is the $x$-value, and the second is the $y$-value.

2. Apply the transformation: The transformation given is $h(x) = f(2x - 3)$, which affects the $x$-coordinate. To find the new $x$-coordinate, we solve for $x$ in the expression $2x - 3$.

   Substituting $x = -1$ into $2x - 3$: $2(-1) - 3 = -2 - 3 = -5$ So, $x = -5$ is the transformed $x$-coordinate.

3. Keep the $y$-coordinate the same, as it is defined by $h(x) = 0$. Thus, the point $(-1, 0)$ transforms to $(-5, 0)$ under the function $h(x) = f(2x - 3)$.

Resulting point:

The transformed point on $h(x)$ is $(-5, 0)$.

Would you like more details or have any questions?

---

Here are 5 related questions you could explore:

1. How would the transformation affect a point like $(2, 3)$?
2. What does the transformation $h(x) = f(2x - 3)$ do geometrically to the graph of $f(x)$?
3. How would a vertical shift (e.g., $h(x) = f(2x - 3) + 2$) affect the point $(-1, 0)$?
4. How do transformations of the form $h(x) = f(ax + b)$ impact the domain of $f(x)$?
5. How would you find the inverse of the transformation $h(x) = f(2x - 3)$?

Tip: Horizontal transformations involving $2x - 3$ include both a horizontal stretch/compression (due to the factor of 2) and a horizontal shift (due to the $-3$).