Consider the function y = \sqrt[3]{x}.
Complete the table of values. Round any values to two decimal places if necessary.
| x | -100 | -10 | -8 | -3 | -1 | 0 | 1 | 3 | 8 | 10 | 100 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| y |
Sketch the graph of y = \sqrt[3]{x}.
Is y = \sqrt[3]{x} an increasing function or a decreasing function?
Is there any restriction on the value of x?
State the range of the function.
Does y = \sqrt[3]{x} have a limiting value?
Does y = \sqrt[3]{x} have an asymptote?
As x gets larger and larger, what value does y approach?
For x \geq 0, describe the rate of increase of the function as x increases.
For x \geq 0, describe the rate of describe the rate of increase of the function as x increases.
Consider the function y = - \sqrt[3]{x}.
Complete the table of values. Round any values to two decimal places if necessary.
| x | -100 | -10 | -8 | -3 | -1 | 0 | 1 | 3 | 8 | 10 | 100 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| y |
Sketch the graph of the function.
Can the function values ever be positive?
Can the function value ever be 0?
State the domain of the function.
State the range of the function.
Is y = - \sqrt[3]{x} an increasing function or a decreasing function?
Consider the function y = \sqrt[3]{ - x }.
Complete the table of values. Round any values to two decimal places if necessary.
| x | -100 | -10 | -8 | -3 | -1 | 0 | 1 | 3 | 8 | 10 | 100 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| y |
Sketch the graph of y = \sqrt[3]{ - x }.
Is y = \sqrt[3]{ - x } an increasing function or a decreasing function?
State the domain of the function.
State the range of the function.
As x approaches -\infty, what does y approach?
As x approaches \infty, what does y approach?
Consider the function y = \sqrt[3]{x} + 3.
Can y ever be negative?
As x gets larger and larger, what value does y approach?
Determine the y-intercept of the curve.
How many x-intercepts does it have?
Sketch the graph of y = \sqrt[3]{x} + 3.
Consider the function y = - 5 \sqrt[3]{x}.
State the domain of the function.
State the range of the function.
Sketch the graph of y = - 5 \sqrt[3]{x}.
Consider the function f \left(x\right) = \sqrt[3]{x-1}.
Complete following table of values:
| x | -7 | 0 | 1 | 2 | 9 |
|---|---|---|---|---|---|
| \sqrt[3]{x-1} | -2 |
Sketch the graph of the function.
State the domain of the function.
State the range of the function.
Consider the function f \left(x\right) = \sqrt[3]{x}-1.
Complete following table of values:
| x | -8 | -1 | 0 | 1 | 8 |
|---|---|---|---|---|---|
| \sqrt[3]{x}-1 | -3 |
Sketch the graph of the function.
State the domain of the function.
State the range of the function.
Consider the following functions:
Sketch the graph of the function.
State the domain of the function.
State the range of the function.
Describe how the function y = 5 \sqrt[3]{x} differs from y = \sqrt[3]{x}.
State the domain and range of y = \sqrt[3]{x} - 4.
Consider the function y = \sqrt[3]{x - 4}.
State the domain of the function.
State the range of the function.
Compare the rate of increase of y = \sqrt[3]{x - 4} and y = \sqrt[3]{x}.