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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Let x= number rows
Then x + 5 = number of seats per row
x(x+5) = 126
X^2 + 5x = 126
x^2 + 5x -126 = 0; now factor or use quadratic:
(x+14)(x-9) = 0; so the answers are either -14, or 9, and since -14 is not possible in this case because you can't have a negative number of rows, the answer is 9 rows.
Check work: number of rows = 9, number of seats per row = 9+ 5= 14, and 9 x 14 = 126
Answer:
y = 5, -4
Step-by-step explanation:
To solve proportions you cross-multiply.
Now that we have 8 = y^2 - y - 12, we must make the entire trinomial equal to 0 by subtracting 8 from both sides.
y^2 - y - 20 = 0
Factor the trinomial.
(y - 5)(y + 4) = 0
Make both factors equal to 0 to solve for both values of y.
- y - 5 = 0 --> y = 5
- y + 4 = 0 --> y = -4
y = 5, -4
Answer:
1 and 2
Step-by-step explanation:
1^2 + 2^2 =
1 + 4 = 5
Total number of outcomes of 7 from 10 = 10*9*8 / 3*2*1 = 120
probability of each outcoe is 0.85^7* (0.15)^(3) = 0.0010819
Required probability = 120 * 0.0010819 = 0.1298
