Question

How can the graph of f(x) = 5(x+5) - 3 be obtained from the graph of y = x??

Answer 1

Answer:

Shift horizontally 5 units to the left, shrink it vertically by a factor of 1/2, shift it 3 units down.

Explanation:

Given the function;

$\begin{gathered} f(x)=\frac{1}{2}(x+5)^2-3\text{ ------1} \\ \text{and} \\ y=x^2\text{ --------2} \end{gathered}$

We want to determine how to derive the graph of equation 1 from equation 2.

Firstly, 5 units to the left will give;

$y=(x+5)^2$

followed by a vertical shrink of factor 1/2 to give;

$y=\frac{1}{2}(x+5)^2$

Then lastly, 3 units down to give;

$y=\frac{1}{2}(x+5)^2-3$

Therefore, the change is;

Shift horizontally 5 units to the left, shrink it vertically by a factor of 1/2, shift it 3 units down.