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Given a(x)=8x

, if a(x)
is vertically stretched by a factor of 4 and reflected across the y-axis, what is the new expression of a(x)
?(1 point)
Responses

a(x)=−4⋅8−x
a left parenthesis x right parenthesis equals negative 4 times 8 superscript negative x baseline

a(x)=8x−4
a left parenthesis x right parenthesis equals 8 superscript x baseline minus 4

a(x)=8−4x
a left parenthesis x right parenthesis equals 8 superscript negative 4 x baseline

a(x)=4⋅8−x

1 answer

To find the new expression of \( a(x) = 8x \) after applying the transformations of being vertically stretched by a factor of 4 and reflected across the y-axis, we can follow these steps:

  1. Vertical Stretch: A vertical stretch by a factor of 4 means we multiply the entire function by 4. Thus, the function becomes: \[ a(x) = 4 \cdot (8x) = 32x \]

  2. Reflection Across the Y-axis: Reflecting the function across the y-axis means we replace \( x \) with \( -x \). So, we replace \( x \) in \( 32x \): \[ a(x) = 32(-x) = -32x \]

Combining these transformations together, the new expression is: \[ a(x) = -32x \]

However, the provided choices don't seem to match this exact transformation. Let's evaluate the options given:

  1. Option 1: \( a(x) = -4 \cdot 8^{-x} \)
  2. Option 2: \( a(x) = 8^{-x} - 4 \)
  3. Option 3: \( a(x) = 8^{-4x} \)
  4. Option 4: \( a(x) = 4 \cdot 8^{-x} \)

The transformations we applied resulted in \( a(x) = -32x \), which means none of the provided options exactly match this transformation. If \( 32x \) or \( 4 \cdot 8^{-x} \) to further adjust, we'd still be left on the mismatched option side.

Could you check for further clarifications on the options?