Do the following graphed functions have an even or odd power?
Consider the function y = x^{2}.
Sketch the curve on a number 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 graph of y = x^{3}:
As x becomes larger in the positive direction (ie x approaches infinity), what happens to the corresponding y-values?
As x becomes larger in the negative direction (ie x approaches negative infinity), what happens to the corresponding y-values?
Consider the functions y = x^{2}, y = x^{4} and y=x^6.
Describe the general shape of the graph of each function.
Sketch the graph of y = x^{2}, y = x^{4} and y=x^6 on the same number plane.
Describe what happens to the graph of a function of the form y=x^{2n} as n increases.
Consider the functions f \left( x \right) = - x^{4} and g \left( x \right) = - x^{6}.
Graph f \left( x \right) = - x^{4} and g \left( x \right) = - 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} on the same set of axes.
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}.
Consider the function y = 2 x^{2}.
Complete the following table of values:
| x | - 2 | - 1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y |
Sketch the graph of y = 2 x^{2}.
For y = a x^{2}, as a increases, how does it change the graph of y = x^{2}?
Consider the curve y = x^{3} - 8.
Find the x-intercept.
Find the y-intercept.
Find the horizontal point of inflection.
Sketch the graph of the curve.
The graph of y = x^{4} has been provided on the following coordinate axes:
Sketch the graph of y = \dfrac{1}{2} x^{4}.
Consider the function y = x^{4} - 4.
Complete the table of values for y = x^{4}:
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y |
Use the graph of y = x^{4} to sketch the graph of y = x^{4} - 4.
What is the y-intercept of the graph \\ y = x^{4} - 4?
What type of transformation occurs on the graph when adding a constant to the equation y = x^{4}?
Consider the function y = - x^{5} - 5.
Sketch the general shape of the function y = - x^{5}.
Sketch the graphs of y = - x^{5} and y = - x^{5} - 5 on the same number plane.
What is the y-intercept of the graph y = - x^{5} - 5?
Consider the function y = \left(x - 2\right)^{2}.
Complete the following table of values:
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y |
Sketch the graph of y = \left(x - 2\right)^{2}.
What is the minimum y-value?
What x-value corresponds to this minimum y-value?
State the coordinates of the vertex.
Consider the quadratic function y = - \left(x + 2\right)^{2} - 6.
Calculate the y-value of the y-intercept.
Is the graph concave up or concave down?
What is the maximum y-value?
What x-value corresponds to the maximum y-value?
State the coordinates of the vertex.
Sketch the graph the parabola.
What is the axis of symmetry of the parabola?