Transform One Function Graph into Another
Read this topicExplanations 3
- In the previous lessons, we've talked about vertical translations, horizontal translations, vertical reflections, horizontal reflections, vertical dilations, and horizontal dila…
By Anusha Rahman, Gabi Slizewska
- (Video) Quadratics with Multiple Transformations by Brian McLogan In this video, Brian McLogan teaches you how to graph a quadratic function in vertex form, with multiple functi…
By Anusha Rahman
- Transform One Function Graph into Another Now that we've learned the individual function transformations, we can combine transformations. When working with functions, you can tr…
By Anusha Rahman
Problems 23
- Let fff and ggg be functions. For which of the following can ggg be expressed as the result of using transformation(s) on fff?
- Is it possible, using transformations (translation, rotation, stretching, etc.), to turn f(x)=x3f(x) = \sqrt[3]{x}f(x)=3x into g(x)=xg(x) = \sqrt{x}g(x)=x?
- If f(x)=x2+3f(x)=x^2+3f(x)=x2+3 what is g(x)g(x)g(x)?
- If f(x)=x+1f(x)=x+1f(x)=x+1 what is g(x)g(x)g(x)?
- If f(x)=12∣3x∣+5f(x)=\frac12|3x|+5f(x)=21∣3x∣+5 what is g(x)g(x)g(x)?
- If f(x)=x3f(x)=x^3f(x)=x3 what is g(x)g(x)g(x)?
- Start with the graph of y=xy = \sqrt{x}y=x in a 3×93\times 93×9 rectangular picture, ranging over x∈[0,9]x\in [0,9]x∈[0,9] and y∈[0,3]y\in [0,3]y∈[0,3]. Now suppose you used MS…
- The graph of y=9x2y = 9x^2y=9x2 can be obtained by vertically stretching the graph of y=x2y = x^2y=x2 by a factor of 999. It can also be obtained by...
- Start with the graph of y=3xy = 3xy=3x in a 9×39\times 39×3 rectangular picture, ranging over x∈[0,3]x\in [0,3]x∈[0,3] and y∈[0,9]y\in [0,9]y∈[0,9]. Now suppose you used MS Pain…
- Now, what is the new function?
- Describe how to obtain the function f(x)=4(x−2+45)f(x)=4\left(\sqrt{x-2}+\frac{4}{5}\right)f(x)=4(x−2+54).
- Which of the following f(x)f(x)f(x) and g(x)g(x)g(x) could be transformations of each other?
- Which of the following f(x)f(x)f(x) and g(x)g(x)g(x) could be transformations of each other?
- Which of the following f(x)f(x)f(x) and g(x)g(x)g(x) could be transformations of each other?
- Now, what is the new function?
- Now, what is the new function?
- Now, what is the new function?
- Describe how to obtain the function f(x)=(5x−6)13−5f(x)=(5x-6)^{\frac{1}{3}}-5f(x)=(5x−6)31−5.
- Describe how to obtain the function f(x)=1x−2+1f(x)=\frac{1}{x-2}+1f(x)=x−21+1.
- Describe how to obtain the function f(x)=411x+7f(x)=\frac{4}{11}x+7f(x)=114x+7.
- The graph of y=8x3y = 8x^3y=8x3 can be obtained by vertically stretching the graph of y=x3y = x^3y=x3 by a factor of 888. It can also be obtained by...
- The graph of y=∣15x∣y = |\frac{1}{5}x|y=∣51x∣ can be obtained by vertically compressing the graph of y=∣x∣y = |x|y=∣x∣ by a factor of 555. It can also be obtained by...
- If f(x)=3xf(x)=3^xf(x)=3x what is g(x)g(x)g(x)?