Consider the same transformation
ℎ
(
𝑥
)
=
𝑓
(
2
𝑥
−
3
)
h(x)=f(2x−3). Transform the point
(
−
1
,
0
)
(−1,0) and select the resulting point on
ℎ
(
𝑥
)
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?

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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 \( -3 \)).

Consider the same transformation h(x) = f(2x - 3). Transform the point (-1, 0) and select the resulting point on h(x).

Explore how to transform the point (-1, 0) using the function h(x) = f(2x - 3). This problem covers important concepts in function transformations, such as horizontal stretching and shifting. Perfect for students in Grades 9-11 looking to deepen their understanding of algebra.

Math Problem Statement

Consider the same transformation ℎ ( 𝑥 )

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