2. Determine if the function is Odd Even Neither. [6] f(x) = -3x4 + 2x3 – 5x2 + x
1 answer:
Answer:
neither
Step-by-step explanation:
• If f(x) = f(- x) then f(x) is even
• If f(- x) = - f(x) then f(x) is odd
Given
f(x) = - 3 + 2x³ - 5x² + x , then
f(- x) = - 3 + 2(- x)³ - 5(- x)² + (- x) = - 3
- 2x³ - 5x² - x
Since f(x) ≠ f(- x) then f(x) is not Even
- f(x) = - (- 3 + 2x³ - 5x² + x) = 3
- 2x³ + 5x² - x
Since f(- x) ≠ - f(x) then f(x) is not Odd
Thus f(x) is neither even nor odd
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The statements about the function that are true are
- The vertex of the function is at (–3,–16).
- The graph is increasing on the interval x > –3.
- The graph is positive only on the intervals where x < –7 and where x > 1.
The equation of the graph is given as
f(x) = (x - 1)(x + 7)
The graph of the function is added as an attachment
On the graph, we have
Vertex = (-3, -16)
This is so because the graph has a minimum point of (-3, -16)
Also, the graph crosses the x-axis at x = 1 and x = -7
This means that the graph is positive at x >1 and x >-7
Because the vertex is a minimum, the graph is increasing at the left of its symmetry i.e. x > -3
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