Question

state domain and range, intercepts, relative max and relative mins points and values, intervals of increase and decrease, intervals of positive and negative, symmetry, and end behavior

Answer 1

The domain of the graph is -∝ < x < ∝ and the range of the graph is -∝ < y < ∝. Also, the graph has no axis of symmetry

The domain and range of the graph

From the graph, we can see that the x values extend indefinitely

So, the domain of the graph is -∝ < x < ∝

From the graph, we can see that the y values extend indefinitely

So, the range of the graph is -∝ < y < ∝

The intercepts

This is where the graph crosses the axes

So, we have the intercepts to be

• x-intercept = -4, -2 and 2
• y-intercept = -9

Relative max and relative mins points and values,

The graph has a relative maximum at (3, 3) and the relative minimum are (0.5, 10)

Intervals of increase and decrease,

There are the intervals where the function increases and decreases

So, we have the intervals to be

• Increasing interval: (0.5, ∝) and (-∝, -3)
• Decreasing interval: (-3, 0.5)

Intervals of positive and negative,

There are the intervals where the function is positive and negative

So, we have the intervals to be

• Positive interval: (-4, -2) and (2, ∝)
• Negative interval: (-∝, -4) and (-2, 2)

The symmetry

This is the line that divides the graph equal part

In this case, the graph has no axis of symmetry

The end behavior

Using the intervals where the function is positive and negative, the end behavior is

• As x ⇒ ∝, f(x) ⇒ +∝
• As x ⇒ -∝, f(x) ⇒ -∝

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