The transformation of a function may involve any change. The correct option is D.
<h3>How does the transformation of a function happen?</h3>
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
- Left shift by c units, y=f(x+c) (same output, but c units earlier)
- Right shift by c units, y=f(x-c)(same output, but c units late)
Vertical shift
- Up by d units: y = f(x) + d
- Down by d units: y = f(x) - d
Stretching:
- Vertical stretch by a factor k: y = k \times f(x)
- Horizontal stretch by a factor k: y = f(\dfrac{x}{k})
Given the function f(x)=2ˣ, while the h(x)=-3(2ˣ), therefore, the function f(x) is a reflection and a translation of a function. Hence, the correct option is D.
Learn more about Transforming functions:
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Answer:
<u>u ≤ -6</u>
Step-by-step explanation:
Given :
Add 2 on both sides :
- 22 + 2 ≤ -4u - 2 + 2
- -4u ≥ 24
Divide both sides by -4 (remember the sign changes direction when divided by a negative number) :
- -4u/-4 ≥ 24/-4
- <u>u ≤ -6</u>
Answer: 2.7
Step-by-Step Explanation:
4xAnswer: y=9-4x
Step-by-step explanation: Subtract 4X from both sides
