Answer:
Let the parent function be given below as
[tex]f(x)=x^2[/tex]
A) reflection over the x-aixs
The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same
[tex]x^2\Rightarrow-x^2[/tex]
B) Horizontal stretch by a factor of 5
A horizontal stretch or shrink by a factor of 1/k means that the point (x, y) on the graph of f(x) is transformed to the point (x/k, y) on the graph of g(x).
[tex]-x^2\Rightarrow-(\frac{1}{5}x^2)[/tex]
C) Vertical shift down 3 units
When a function shifts vertically, the y-value changes. The x-value stays the same, while the y-value changes the amount of the shift. If it shifts up, then we add the value to the y-term. If it shifts down, we will subtract that value from the y-term.
[tex]-(-\frac{1}{5}x^2)\Rightarrow-(\frac{1}{5}x^2)-3[/tex]
Graphically, it can be represented as
Hence,
The function of g(x) is given below as
[tex]g(x)=-(\frac{1}{5}x^2)-3[/tex]
