Power Functions with Any Exponent
Read this topicExplanations 3
- (Video) Power Functions and Their Graphs by ProfessorRosever In this video by ProfessorRosever a power function is defined.
By Stefan Cuevas, Alex Federspiel
- (Video) Power Functions and Their Properties by Math Easy Solutions In this video by Math Easy Solutions power functions are defined and their properties are described.
By Stefan Cuevas, Alex Federspiel
- Power Functions Power functions are functions that are raised to a power, aaa. aaa is a constant. We have seen power functions before, such as with quadratic functions and cubic…
By Anusha Rahman
Problems 30
- Let f(x)=5x2f(x) = 5x^2f(x)=5x2 and g(x)=3x3g(x) = 3x^3g(x)=3x3. What is (fg)(x)(fg)(x)(fg)(x)?
- Let fff and ggg be functions such that f(x)=3x4f(x) = 3x^4f(x)=3x4 and (fg)(x)=12x12(fg)(x) = 12x^{12}(fg)(x)=12x12. If g(x)=axbg(x) = ax^bg(x)=axb, what are the values of aaa a…
- Let f(x)=3x3α−4+xαf(x) = \sqrt{3x^{3\alpha - 4}} + x^\alphaf(x)=3x3α−4+xα for some constant α\alphaα. If fff is a power function (i.e. can be expressed in the form f(x)=axbf(x)…
- What is the long-run behavior of the function f(x)=x4f(x) = x^4f(x)=x4? Select all that hold true.
- What is the long-run behavior of the function f(x)=x6f(x) = x^6f(x)=x6? Select all that hold true.
- What is the long-run behavior of the function f(x)=x3f(x) = x^3f(x)=x3? Select all that hold true.
- What is the long-run behavior of the function f(x)=x5f(x) = x^5f(x)=x5? Select all that hold true.
- What is the long-run behavior of the function f(x)=−x2f(x) = -x^2f(x)=−x2? Select all that hold true.
- What is the long-run behavior of the function f(x)=−x4f(x) = -x^4f(x)=−x4? Select all that hold true.
- What is the long-run behavior of the function f(x)=−x7f(x) = -x^7f(x)=−x7? Select all that hold true.
- What is the long-run behavior of the function f(x)=−x9f(x) = -x^9f(x)=−x9? Select all that hold true.
- Find the power function h(x)=g(x)f(x)h(x) = g(x)f(x)h(x)=g(x)f(x), where g(x)=5xg(x) = 5xg(x)=5x and f(x)=10x2f(x) = 10x^2f(x)=10x2.
- Find the power function h(x)=g(x)f(x)h(x) = g(x)f(x)h(x)=g(x)f(x), where g(x)=5x12g(x) = 5x^{\frac{1}{2}}g(x)=5x21 and f(x)=10x2f(x) = 10x^2f(x)=10x2 for positive xxx.
- Find the power function h(x)=g(x)f(x)h(x) = \frac{g(x)}{f(x)}h(x)=f(x)g(x), where g(x)=20x5g(x) = 20x^5g(x)=20x5 and f(x)=10x2f(x) = 10x^2f(x)=10x2.
- Find the power function h(x)=g(x)f(x)h(x) = \frac{g(x)}{f(x)}h(x)=f(x)g(x), where g(x)=20x7g(x) = 20x^7g(x)=20x7 and f(x)=10x2f(x) = 10x^2f(x)=10x2.
- What is the minimum possible value of x4x^4x4?
- If y=z24y=z^{24}y=z24 and x=z1/2 x=z^{1/2}\;x=z1/2 what is the relationship between y and x?
- If y=z1/4y=z^{1/4}y=z1/4 and z=x16 z=x^{16}\;z=x16 what is the relationship between y and x?
- True or False\text{True or False}True or False === The numbers nmn^mnm and mnm^nmn are identical.
- x4=0.0625x^4=0.0625x4=0.0625 What is x3 x^3\;x3?
- Find f(x)g(x)f(x)g(x)f(x)g(x) if f(x)=2x3f(x)=2x^3f(x)=2x3 and g(x)=4x4g(x)=4x^4g(x)=4x4.
- Find f(x)g(x)f(x)g(x)f(x)g(x) if f(x)=6x8f(x)=6x^8f(x)=6x8 and g(x)=3x12g(x)=3x^{12}g(x)=3x12.
- Find f(x)g(x)f(x)g(x)f(x)g(x) if f(x)=11x7f(x)=11x^{7}f(x)=11x7 and g(x)=4x5g(x)=4x^{5}g(x)=4x5.
- Find f(x)g(x)h(x)f(x)g(x)h(x)f(x)g(x)h(x) if f(x)=x2f(x)=x^{2}f(x)=x2, g(x)=x3g(x)=x^{3}g(x)=x3, and h(x)=100x95h(x)=100x^{95}h(x)=100x95.
- Let f(x)=axbf(x)=ax^bf(x)=axb and g(x)=cxdg(x)=cx^dg(x)=cxd where aaa, bbb, ccc, and ddd are positive integers. Find g(x)f(x)g(x)f(x)g(x)f(x).
- Find the inverse of f(x)=0.07x34f(x)=0.07x^{\frac34}f(x)=0.07x43.
- Let f(x)=0.42xaf(x)=0.42x^af(x)=0.42xa where aaa is a nonzero real number. Find aaa if f−1(x)=7.889x1af^{-1}(x)=7.889x^{\frac1a}f−1(x)=7.889xa1.
- True or False\text{True or False}True or False === The function f(x)=(x−1)4f(x)=(x-1)^4f(x)=(x−1)4 is graphed above.
- True or False\text{True or False}True or False === The function f(x)=x45+3f(x)=x^{\frac45}+3f(x)=x54+3 is graphed above.
- True or False\text{True or False}True or False === The function f(x)=−8x8−5f(x)=-8x^8-5f(x)=−8x8−5 is graphed above.