Functions domains and range
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1. Find the average rate of change of f(x)=x^3-9x+9:
a) from -8 to -2
b) from -1 to 1
c) from 1 to 4
a) What is average rate of change of f (x) =x^3-9x+9 from -8 to -2?
2. The function f is defined as follows
f(x) = {4+2x if x<0
{x^2 if x>0
a) Find the domain of the function
b) Locate any intercepts
c) Graph function
d) Based on graph find range
e) Is f continuous on its domain?
a) The domain of the function f is ____.
3. Write the function whose graph is the graph of y=sqrt x, but is shifted to the left 3 units y=____.
4. Write the function whose graph is the graph of y=|x|, but is shifted down 8 units y=____.
5. Write the function whose graph is the graph is the graph of y=(x+4)^2, but is reflected about the y- axis y=____.
6. Write the function whose graph is the graph of y=x^2 but horizontally strectched by a factor of 8; y=____.
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Solution Summary
Some algebra problems related to functions are solved for their domains, range, graph etc.
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>1. Find the average rate of change of f(x)=x^3-9x+9:
f(-8) = (-8)^3 - 9*(-8) + 9 = -431
f(-2) = (-2)^3 - 9*(-2) + 9 = 19
f(-1) = (-1)^3 - 9*(-1) + 9 = 17
f(1) = (1)^3 - 9*(1) + 9 = 1
f(4) = (4)^3 - 9*(4) + 9 = 37
a) from -8 to -2 = (-431 - 19)/(-431) = 1.044
b) from -1 to 1 = (17 - 1)/17 = 0.941
c) from 1 to 4 = (1 - ...
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- BEng, Allahabad University, India
- MSc , Pune University, India
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