Question1. For the graph of $f(x)=\sqrt{x}$ , identify the transformation that would not be applied to

Studdy Solution

STEP 1

1. The function $f(x) = \sqrt{x}$ is the base function.
2. The transformations to consider include horizontal and vertical shifts, stretches, compressions, and reflections.
3. We need to identify which transformation is not applied to obtain $y = 2f(-2x) - 3$ .

STEP 2

1. Identify the transformations applied to $f(x)$ .
2. Analyze each transformation step-by-step.
3. Determine which transformation is not applied.

STEP 3

Identify the transformations applied to $f(x) = \sqrt{x}$ to obtain $y = 2f(-2x) - 3$ .
The given function is $y = 2f(-2x) - 3$ . Let's break it down:
1. $f(-2x)$ involves a horizontal transformation.
2. $2f(-2x)$ involves a vertical transformation.
3. $2f(-2x) - 3$ involves another vertical transformation.

STEP 4

Analyze each transformation step-by-step:
1. Horizontal Reflection and Compression: - The expression $f(-2x)$ indicates a horizontal reflection across the y-axis and a horizontal compression by a factor of $\frac{1}{2}$ .
2. Vertical Stretch: - The expression $2f(-2x)$ indicates a vertical stretch by a factor of 2.
3. Vertical Shift: - The expression $2f(-2x) - 3$ indicates a vertical shift downward by 3 units.

STEP 5

Determine which transformation is not applied:
The transformations applied are: - Horizontal reflection across the y-axis. - Horizontal compression by a factor of $\frac{1}{2}$ . - Vertical stretch by a factor of 2. - Vertical shift downward by 3 units.
The transformation that is not applied is: - Horizontal shift.
The transformation that would not be applied to $f(x)$ to obtain the graph of $y = 2f(-2x) - 3$ is a horizontal shift.

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