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We know that the polynomial function is of degree 3, and that its roots are -4, 0, 2.
With this data we can write a generic equation for the function:
f (x) = bx (x + 4) (x-2)
Since the function is of degree 3 and cuts the axis at x = 0, then it has rotational symmetry with respect to the origin.
The graph of the function can be of two main forms, based on the value of the coefficient b.
If b is positive then the function grows from y = -infinite and cuts the x-axis for the first time in -4. Then it decreases, cuts at x = 0 and begins to grow again cutting the x-axis for the third time at x = 2. and continues to grow until y = infnit
If b is negative, then the function decreases from y = infinity and cuts the x-axis for the first time in -4. Then it grows, cuts at x = 0 and begins to decrease again by cutting the x-axis for the third time at x = 2, and continues to decrease until y = -infnit.
In the attached images the graphs of the function f (x) are shown assuming b = -1 and b = 1
Answer:
y=0.3x
Step-by-step explanation:
Formula =
y α x
y = kx
Where k is the constant of proportionality.
When y = 1.5; x = 5;
We substitute these known values in the equation,
y = kx
1.5 = k5
Dividing both sides of the equation by 5 to find the value for k, we have
1.5/5= k0.3/5
Therefore,
K = 0.3
Having found the value of k,
We substitute this value into the relationship
y = kx
Therefore we have,
y = 0.3x.
The direct variation function is therefore,
y = 0.3x.
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