3.02 Power functions
Do the following graphed functions have an even or odd power?
Consider the function y = x^{2}.
Complete the following table of values:
| x | - 3 | - 2 | - 1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|
| y |
Using the points in the table, plot the curve on a cartesian plane.
Are the y-values ever negative?
Write down the equation of the axis of symmetry.
What is the minimum y-value?
For every y-value greater than 0, how many corresponding x values are there?
Consider the function f \left( x \right) = - x^{2}.
Does the graph rise or fall to the right?
Does the graph rise or fall to the left?
Consider the functions f(x) = - x^{4} and g(x) = - x^{6}.
Graph f(x) = - x^{4} and g(x) = - x^{6} on the same set of axes.
Which of the above functions has the narrowest graph?
Consider the functions f(x) = x^{3} and g(x) = x^{5}.
Graph f(x) = x^{3} and g(x) = x^{5}.
How would the graph of y = x^{7} differ to the graph of f(x) = x^{3} and g(x) = x^{5} ?
Consider the function y = x^{7}.
As x approaches infinity, what happens to the corresponding y-values?
As x approaches negative infinity, what happens to the corresponding y-values?
Sketch the general shape of y = x^{7}.
Sketch the general shape of y = - x^{7}.