Question

1. jared graphed three points to create d(x). he then multiplied all of the output values by a constant value to create a(x).

x	d(x)
1	16
3	10
5	-8
x	a(x)
1	8
3	5
5	-4

a. what factor did he multiply the output values of d(x) by to get a(x)?
b. did he create a vertical stretch or vertical shrink? how do you know?
describe how each new function is related to the given parent function.

1. parent function: f(x)=|x|

new function: w(x)=7|x|

1. parent function: f(x)=√x

new function: m(x)=-√(1/4)x

1. parent function: f(x)=x²

new function: p(x)=-1.5x²

1. parent function: f(x)=x

new function: d(x)=0.4x
describe all transformations that occur on the function f(x).

1. 3f(x)+4
2. (2/3)f(x - 2)
3. f(1.25x)-7
4. (7/6)f(-3 + x)

Explanation:

Step1: Find the multiplication factor

For \(x = 1\), \(\frac{a(1)}{d(1)}=\frac{8}{16}=\frac{1}{2}\). For \(x = 3\), \(\frac{a(3)}{d(3)}=\frac{5}{10}=\frac{1}{2}\). For \(x = 5\), \(\frac{a(5)}{d(5)}=\frac{- 4}{-8}=\frac{1}{2}\).

Step2: Determine the type of transformation

If the factor \(k\) by which the output - values are multiplied satisfies \(0

3.a

The new function \(w(x)=7|x|\) is related to the parent function \(f(x) = |x|\) by a vertical stretch. When we have a function \(y = kf(x)\) and \(k>1\), in this case \(k = 7\), the graph of \(y = f(x)\) is vertically stretched by a factor of \(k\).

For the parent function \(f(x)=\sqrt{x}\) and the new function \(m(x)=-\sqrt{\frac{1}{4}x}\), first, there is a horizontal stretch by a factor of 4 (because of the \(\frac{1}{4}x\) inside the square - root. When we have \(y = f(bx)\) and \(0 < b<1\), the graph is horizontally stretched by a factor of \(\frac{1}{b}\), here \(b=\frac{1}{4}\) so the stretch factor is 4). Also, there is a reflection about the \(x\) - axis due to the negative sign in front of the square - root.

For the parent function \(f(x)=x^{2}\) and the new function \(p(x)=-1.5x^{2}\), there is a vertical stretch by a factor of 1.5 (since \(|k| = 1.5>1\) in \(y = kf(x)\)) and a reflection about the \(x\) - axis due to the negative sign.

Answer:

\(\frac{1}{2}\)

3.b