Question

What transformation was not done to the linear parent function, f(x) = x, to get the function g%28x%29%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%28x-3%29%2B7" id="TexFormula1" title="g(x) = -\frac{1}{2}(x-3)+7" alt="g(x) = -\frac{1}{2}(x-3)+7" align="absmiddle" class="latex-formula">?
A. Shifted left 3 units
B. Vertically compressed by a factor of 2
C. Reflected over the x-axis
D. Shifted up 7 units

Answer 1

Answer:

The transformation was not done is Shifted left 3 units

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

- A vertical stretching is the stretching of the graph away from

 the x-axis

- A vertical compression is the squeezing of the graph toward

 the x-axis.

- if k > 1, the graph of y = k•f(x) is the graph of f(x) vertically

  stretched by multiplying each of its y-coordinates by k.

- if 0 < k < 1 (a fraction), the graph is f(x) vertically compressed

 by multiplying each of its y-coordinates by k.

- if k should be negative, the vertical stretch or compress is

 followed by a reflection across the x-axis.  

* now lets solve the problem

∵ f(x) = x

∵ g(x) = -1/2 (x - 3) + 7

# -1/2 means the graph is vertically compressed by a factor of 2

  and reflected over the x-axis

# x - 3 means the graph shifted to the right 3 units

# + 7 means the graph shifted up 7 units

* The transformation was not done is Shifted left 3 units