Question

Describe the graph of the function g(x)=(x-1)(x+4)^3(x+5)^2

The graph

The axis at (1,0)

Crosses
Doesn’t intersect
Touches

The axis at -4,0
Crosses
Doesn’t intersect
Touches

The axis at -5,0
Crosses
Doesn’t intersect
Touches

Answer 1

• crosses at (1, 0)
• crosses at (-4, 0)
• touches at (-5, 0)

Explanation:

The worksheet tells you the answers.

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If the power of (x -k) is odd, the graph crosses the axis.

factors (x -1) and (x +4)^3 have odd powers, so the graph crosses where these factors are zero

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If the power of (x -k) is even, the graph touches the axis.

factor (x +5)^2 has an even power, so the graph touches where that factor is zero.