Question

# g is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to g. (c) Ske

Transformations of functions

g is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to g. (c) Sketch the graph of g by hand. (d) Use function notation to write g in terms of the parent function f. $$\displaystyle{g{{\left({x}\right)}}}=\frac{{1}}{{2}}∣{x}−{2}∣−{3}$$

2021-05-28

a)Parent function: $$f(x)=|x|$$
b)-Vertical shrink by a factor of $$\displaystyle\frac{{1}}{{2}}$$
-Horizontal shift 2 units to the right
-Vertical 3 units downward
c)The graph will be:
[Graph]
d)In function notation, $$\displaystyle{g{{\left({x}\right)}}}={\left(\frac{{1}}{{2}}\right)}{f{{\left({x}-{2}\right)}}}-{3}$$ <- Answer