Solve. 4/3-3x+5/2=-6x+5/6
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The transformation of a function may involve any change. The function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
<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})
The function f(x)=x^(1/3) is transformed to form the function of h(x)=(2x)^(1/3)+5. Therefore, the transformation made to the function is,
Vertically stretched by a factor of 2^(1/3) ⇒ 2^(1/3) × x^(1/3) = (2x)^(1/3)
Up by 5 units ⇒ (2x)^(1/3) + 5
Hence, the function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
Learn more about Transforming functions:
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Answer:
C,
Step-by-step explanation:
Euler's formula:
Looking at the expression in the parentheses, your x is explicitly given to you as , so using Euler's formula:
Which is C.
The inequality is used to solve how many hours of television Julia can still watch this week is
The remaining hours of TV Julia can watch this week can be expressed is 3.5 hours
<h3><u>Solution:</u></h3>Given that Julia is allowed to watch no more than 5 hours of television a week
So far this week, she has watched 1.5 hours
To find: number of hours Julia can still watch this week
<em>Let "x" be the number of hours Julia can still watch television this week</em>
"no more than 5" means less than or equal to 5 ( ≤ 5 )
Juila has already watched 1.5 hours. So we can add 1.5 hours and number of hours Julia can still watch television this week which is less than or equal to 5 hours
number of hours Julia can still watch television this week + already watched ≤ Total hours Juila can watch
Thus the above inequality is used to solve how many hours of television Julia can still watch this week.
Solving the inequality,
Thus Julia still can watch Television for 3.5 hours