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Vertical & Horizontal Translations

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Practice: Vertical & Horizontal Translations

Let f(x)=x3f(x)=x^3.

True or False:
The graph of the transformed function f(x)=2(x−1)3+1f(x)=2(x-1)^3+1 will affect the range of the function.
More Translations Questions:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let (a,b) (a, b)~be some point on the function y=f(2x+4)+3y=f(2x+4)+3.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let (3,−5) (3, -5)~be some point on the function y=−f(1−x)+3y=-f(1-x)+3.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let f(x)=x2f(x)=x^2.
True or False:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
The function y=f(x) y=f(x)~has been transformed to y=f(x−h)+ky=f(x-h)+k. Determine the values of h and k for each of the following transformations:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
The function y=f(x) y=f(x)~has been transformed to y=f(x−h)+ky=f(x-h)+k. Determine the values of h and k for each of the following transformations:
More Domain & Range Questions:
Domain and Range
Determine the domain for the function y=4xx2+5x+6y=\dfrac{4x}{x^2+5x+6}.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let f(x)=x2f(x)=x^2.
True or False:
Domain and Range
Determine the domain for the function y=4xx2+5x+6y=\dfrac{4x}{x^2+5x+6}.
Practice: Domain & Range
Find the domain & range of the following function shown below:
Practice: Domain & Range
Find the domain & range of the following function shown below:
Domain & Range
Practice: Domain & Range
Match the function with its appropriate domain or range.
Domain & Range
Practice: Domain & Range
Match the function with its appropriate domain or range.
Domain & Range
Practice: Domain & Range
Find the range of y=−(x+5)2+1y=-(x+5)^2+1.
Domain & Range
Practice: Domain & Range
Find the range of y=6x2−10y=6x^2-10.
More Translations Questions:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let (a,b) (a, b)~be some point on the function y=f(2x+4)+3y=f(2x+4)+3.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let (3,−5) (3, -5)~be some point on the function y=−f(1−x)+3y=-f(1-x)+3.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let f(x)=x2f(x)=x^2.
True or False:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
The function y=f(x) y=f(x)~has been transformed to y=f(x−h)+ky=f(x-h)+k. Determine the values of h and k for each of the following transformations:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
The function y=f(x) y=f(x)~has been transformed to y=f(x−h)+ky=f(x-h)+k. Determine the values of h and k for each of the following transformations:
More Determining Domain & Range Questions:
Domain and Range
Determine the domain for the function y=4xx2+5x+6y=\dfrac{4x}{x^2+5x+6}.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let f(x)=x2f(x)=x^2.
True or False:
Domain and Range
Determine the domain for the function y=4xx2+5x+6y=\dfrac{4x}{x^2+5x+6}.
Practice: Domain & Range
Find the domain & range of the following function shown below:
Practice: Domain & Range
Find the domain & range of the following function shown below:
Domain & Range
Practice: Domain & Range
Match the function with its appropriate domain or range.
Domain & Range
Practice: Domain & Range
Match the function with its appropriate domain or range.
Domain & Range
Practice: Domain & Range
Find the range of y=−(x+5)2+1y=-(x+5)^2+1.
Domain & Range
Practice: Domain & Range
Find the range of y=6x2−10y=6x^2-10.
More Domain & Range Questions:
Domain and Range
Determine the domain for the function y=4xx2+5x+6y=\dfrac{4x}{x^2+5x+6}.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let f(x)=x2f(x)=x^2.
True or False:
Domain and Range
Determine the domain for the function y=4xx2+5x+6y=\dfrac{4x}{x^2+5x+6}.
Practice: Domain & Range
Find the domain & range of the following function shown below:
Practice: Domain & Range
Find the domain & range of the following function shown below:
Domain & Range
Practice: Domain & Range
Match the function with its appropriate domain or range.
Domain & Range
Practice: Domain & Range
Match the function with its appropriate domain or range.
Domain & Range
Practice: Domain & Range
Find the range of y=−(x+5)2+1y=-(x+5)^2+1.
Domain & Range
Practice: Domain & Range
Find the range of y=6x2−10y=6x^2-10.
More Vertical & Horizontal Translations Questions:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let (a,b) (a, b)~be some point on the function y=f(2x+4)+3y=f(2x+4)+3.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let (3,−5) (3, -5)~be some point on the function y=−f(1−x)+3y=-f(1-x)+3.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let f(x)=x2f(x)=x^2.
True or False:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
The function y=f(x) y=f(x)~has been transformed to y=f(x−h)+ky=f(x-h)+k. Determine the values of h and k for each of the following transformations:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
The function y=f(x) y=f(x)~has been transformed to y=f(x−h)+ky=f(x-h)+k. Determine the values of h and k for each of the following transformations:
More Translations Questions:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let (a,b) (a, b)~be some point on the function y=f(2x+4)+3y=f(2x+4)+3.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let (3,−5) (3, -5)~be some point on the function y=−f(1−x)+3y=-f(1-x)+3.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let f(x)=x2f(x)=x^2.
True or False:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
The function y=f(x) y=f(x)~has been transformed to y=f(x−h)+ky=f(x-h)+k. Determine the values of h and k for each of the following transformations:
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
The function y=f(x) y=f(x)~has been transformed to y=f(x−h)+ky=f(x-h)+k. Determine the values of h and k for each of the following transformations:
More Domain & Range Questions:
Domain and Range
Determine the domain for the function y=4xx2+5x+6y=\dfrac{4x}{x^2+5x+6}.
Vertical & Horizontal Translations
Practice: Vertical & Horizontal Translations
Let f(x)=x2f(x)=x^2.
True or False:
Domain and Range
Determine the domain for the function y=4xx2+5x+6y=\dfrac{4x}{x^2+5x+6}.
Practice: Domain & Range
Find the domain & range of the following function shown below:
Practice: Domain & Range
Find the domain & range of the following function shown below:
Limits at Infinity: Domain and Range
(Original question is written in long answer. Multiple choice has been used here for convenience)
Let f(x)=x2−6x−3\displaystyle f(x) = \frac{\sqrt{x^2 - 6}}{x - 3}.
Domain & Range
Practice: Domain & Range
Match the function with its appropriate domain or range.
Domain & Range
Practice: Domain & Range
Match the function with its appropriate domain or range.
Domain & Range
Practice: Domain & Range
Find the range of y=−(x+5)2+1y=-(x+5)^2+1.
Domain & Range
Practice: Domain & Range
Find the range of y=6x2−10y=6x^2-10.
Domain & Range
Match the first two functions with their domain, and the second two function with their range.
Domain & Range
Find the range of y=−2x2+5y=-2x^2+5.
Domain and Range
Find the domain and range of f(x)=x+∣x∣xf\left(x\right)=\frac{x+\left|x\right|}{x}.