The equation of the function is f(x) = x(x + 2)(x -1)(x -3)
The function end behavior
From the graph, we have the following highlight:
- As x increases, the function values increase
- As x decreases, the function values increase
The above means that:
f(x) approaches positive infinity irrespective of the x value
Hence, the end behavior of the function is:
[tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:[/tex]
The sign of the leading coefficient
Since, the function opens upward.
Then the sign of the leading coefficient is positive
The zeros of the function
This is the point, where the graph crosses the x-axis.
From the graph, we have the zeros to be:
x = -2, x = 0, x = 1 and x = 3
Since the graph crosses the x-axis at this point, then the multiplicity of the zeros is 1
The equation of the function
In (c), we have:
x = -2, x = 0, x = 1 and x = 3
Rewrite as:
x + 2= 0, x = 0, x - 1 = 0 and x - 3 = 0
Multiply these values
f(x) = x(x + 2)(x -1)(x -3)
Hence, the equation of the function is f(x) = x(x + 2)(x -1)(x -3)
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