Question

Enter the correct answer in the box.The graph of function gis created by applying these transformations to the parent tangent function:• reflection over the x-axis• horizontal stretch by a factor of 5• vertical shift down 3 unitsWrite the equation representing function g

Answer 1

Let the parent function be given below as

`f(x)=x^2`

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

`x^2\Rightarrow-x^2`

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).

`-x^2\Rightarrow-((1)/(5)x^2)`

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.

`-(-(1)/(5)x^2)\Rightarrow-((1)/(5)x^2)-3`

Graphically, it can be represented as

Hence,

The function of g(x) is given below as

`g(x)=-((1)/(5)x^2)-3`