Question

Can anyone help me with this problem. College Calculus 1

Answer 1

Step 1:

When by either

f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.

In general, a vertical stretch is given by the equation

y=bf(x). If b>1, the graph stretches with respect to the y-axis, or vertically. If b<1, the graph shrinks with respect to the y-axis. In general, a horizontal stretch is given by the equation y=f(cx) If c>1, the graph shrinks with respect to the x-axis, or horizontally. If c<1, the graph stretches with respect to the x-axis.

Step 2:

The function is vertically stretched by a factor of 2.

`\begin{gathered} Parent\text{ function} \\ y\text{ = }\sqrt[]{4x-x^2} \\ \text{When a function is stretched by a factor of 2} \\ \text{The new function becomes } \\ y\text{ = 2}\sqrt[]{4x-x^2} \end{gathered}`

Step 3:

A horizontal translation is generally given by the equation

y=f(x−a). These translations shift the whole function side to side on the x-axis.

Hence, the function is translated 6 units to the right

`y\text{ = 2}\sqrt[]{4(x-6)-(x-6)^2}`

Final answer

`\begin{gathered} \text{The function is} \\ \text{y = 2}\sqrt[]{4(x-6)-(x-6)^2} \end{gathered}`