The polynomial X to the 3rd+8 is equal to
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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:
y = 1/3x - 2:
- y - intercept: - 2
- x - intercept: 6
y = 12 - 6x:
- y - intercept: 12
- x - intercept: 2
y = 3x - 7:
- y - intercept: -7
- x - intercept: 7/3
Step-by-step explanation:
Hello!
<h3>Slope Intercept Form</h3>The slope-intercept form of a line is
- y = output, ordinate
- m = slope
- x = input, abscissa
- b = y-intercept
The y-intercept is the "b" value of the line, given as -2.
To find the x-intercept, we simply replace the y-value with 0:
- 0 = 1/3x - 2
- 2 = 1/3x
- 6 = x
y - intercept: - 2
x - intercept: 6
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<h3>y = 12 - 6x</h3>
You can rearrange the equation, y = -6x + 12, to find the y-intercept: 12.
Solving for the x-intercept (remember, replace y with 0):
- 0 = -6x + 12
- -12 = -6x
- 2 = x
y - intercept: 12
x - intercept: 2
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<h3></h3><h3>y = 3x - 7</h3>Simply take the "b" value, -7, to find the y-intercept of -7.
Solve for the x-intercept:
- 0 = 3x - 7
- 7 = 3x
- x = 7/3
y - intercept: -7
x - intercept: 7/3
<u><em>Additional Note:</em></u>
You can also solve for the y-intercept by replacing x with 0. This method can be used for any interests, just plug in the opposite variable from what you are solving for with 0.
The proof is that the x-intercept is the value when the y = 0, the x-axis. You can plug in 0 for y to solve for x. Similarly, when solving for the y-intercept, you plug 0 for x as the y-axis is at x = 0.