Answer to Question #236711 in Algebra for Lara

Question

Let g(x) be the transformation of f(x)= x2. Write the rule for g(x) using the change described.

1. horizontal compression by a factor of 1/5 followed by a vertical shift down 7 units and reflection across y-axis. ______________

2. reflection across the x-axis followed by a vertical stretch by a factor of 3, a horizontal shift 6 units left, and a vertical shift 4 units down. _____________

Answer 1

1)

Parent Function: $f(x) = x\\^2$

There are:

• A horizontal compression by a factor of $\frac{1}{5}$
• A vertical shift down 7 units
• A reflection across y-axis, means that b is negative

The general form for the rule is: $f(x) = a \times f([b(x-h]) + k$

Therefore, $b = -5$ because of horizontal compression by a factor of $\frac{1}{5}$ and reflection across y-axis

k= - 7

Replacing b and k in the general form of the rule $f(x) = a f[ b(x − h)] + k$ where $f(x) = x\\^2$ , we find, $f(x) = (-5(x))\\^2 - 7$

$= f(x) = (-5(x))\\^2 - 7$

2)

Parent Function: $f(x) = x\\^2$

The general form for the rule is: $f(x) = a \times f([b(x-h]) + k$

There are:

Reflection across the x-axis, indicating that $a$ is negative

Vertical stretch by a factor of 3, means that $a= -3$

A horizontal shift 6 units left, means that $h=-6$

 A vertical shift 4 units down, means that $k= -4$

Replacing a, k, and h in the general form of the rule $f(x) = a f[ b(x − h)] + k$ where $f(x) = x\\^2$ , we find $f(x) = -3((x + 6)\\^2) - 4$

$= -3((x + 6)\\^2) - 4$