# Transformation of functions questions and answers Recent questions in Transformations of functions
Transformations of functions
ANSWERED ### If $$f(x) = x + 4$$ and $$\displaystyle{g{{\left({x}\right)}}}={4}{x}²$$, find $$(f + g)(x)$$ and $$(f + g)(2)$$.

Transformations of functions
ANSWERED ### Given that f(x) = 3x - 7 and that (f + g)(x) = 7x + 3, find g(x).

Transformations of functions
ANSWERED ### g is related to one of the parent functions. Describe the sequence of transformations from f to g. $$g(x) = 2 - (x + 5)^2$$

Transformations of functions
ANSWERED ### use long division to determine if 2x-1 is a factor of $$\displaystyle{p}{\left({x}\right)}={6}{x}^{{3}}+{7}{x}^{{2}}-{x}-{2}$$

Transformations of functions
ANSWERED ### $$\displaystyle{f{{\left({x}\right)}}}={9},{\quad\text{if}\quad}{x}\le-{4},{\quad\text{and}\quad}{f{{\left({x}\right)}}}={a}{x}+{b},{\quad\text{if}\quad}-{4}{<}{x}{<}{5},{\quad\text{and}\quad}{f{{\left({x}\right)}}}=-{9},{\quad\text{if}\quad}{x}\ge{5},$$ Find the constants, if the function is continuous on the entire line.

Transformations of functions
ANSWERED ### Graph f and g in the same rectangular coordinate system. Use transformations of the graph off to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range. $$\displaystyle{f{{\left({x}\right)}}}={\ln{{x}}}{\quad\text{and}\quad}{g}⟨{x}{)}=−{\ln{{\left({2}{x}\right)}}}$$

Transformations of functions
ANSWERED ### x=-8, when $$\displaystyle{y}=-\frac{{1}}{{4}}$$ in an inverse variation. Find y, when x=4.

Transformations of functions
ANSWERED ### Describe the transformations that were applied to $$\displaystyle{y}={x}^{{{2}}}$$ to obtain each of the following functions. $$\displaystyle{a}{)}{y}=-{2}{\left({x}-{1}\right)}^{{{2}}}+{23}\ {b}{)}{y}={\left({\frac{{{12}}}{{{13}}}}{\left({x}+{9}\right)}\right)}^{{{2}}}-{14}\ {c}{)}{y}={x}^{{{2}}}-{8}{x}+{16}\ {d}{)}{y}={\left({x}+{\frac{{{3}}}{{{7}}}}\right)}{\left({x}+{\frac{{{3}}}{{{7}}}}\right)}\ {e}{)}{y}={40}{\left(-{7}{\left({x}-{10}\right)}\right)}^{{{2}}}+{9}$$

Transformations of functions
ANSWERED ### Show that f is inverse of g and vice-versa, if f(x)=x-6 and g(x)=x+6

Transformations of functions
ANSWERED ### Given: $$\displaystyle\frac{m}{{8}}=\frac{15}{{24}}$$ Is $$\displaystyle{8}\times{m}={25}\times{15}$$ true or false? Correct if false. Find m.

Transformations of functions
ANSWERED ### Find domain of fog, if 1. $$\displaystyle{f{{\left({x}\right)}}}={x}+{5};{g{{\left({x}\right)}}}=\frac{{7}}{{{x}+{7}}}$$ 2. $$\displaystyle{f{{\left({x}\right)}}}=\sqrt{{x}};{g{{\left({x}\right)}}}={6}{x}+{18}$$

Transformations of functions
ANSWERED ### h is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to h. (c) Sketch the graph of h by hand. (d) Use function notation to write h in terms of the parent function f. h(x)=√x−1+4

Transformations of functions
ANSWERED ### $$\displaystyle{f}:{R}\to{R}$$ f(x)=7x-3 Prove that f is onto.

Transformations of functions
ANSWERED ### 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. $$\displaystyle{g{{\left({x}\right)}}}=−{\left({x}+{3}\right)}^{{3}}−{10}$$

Transformations of functions
ANSWERED ### Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f (x). \begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \ \hline f(x) & -1 & -3 & 4 & 2 & 1 \ \hline \end{array} \begin{array}{|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 0 & 1 \ \hline g(x) & -1 & -3 & 4 & 2 & 1 \ \hline \end{array} \begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \ \hline h(x) & -2 & -4 & 3 & 1 & 0 \ \hline \end{array}

Transformations of functions
ANSWERED ### Sketch a graph of the function. Use transformations of functions whenever possible. $$f(x)=\begin{cases}1-x & if & x<0 \\1 & if & x\geq0\end{cases}$$

Transformations of functions
ANSWERED ### g(x) $$\displaystyle=\frac{{{2}{x}^{{2}}-{3}{x}-{20}}}{{{x}-{4}}},{\quad\text{if}\quad}{x}\ne{4}$$ and =kx-15, if x=4 Evaluate the constant k that makes the function continuous.

Transformations of functions
ANSWERED ### Given: n=3; 4 and 2i are zeros; f(-1)=75 Find an nth-degree polynomial function with real coefficients

Transformations of functions
ANSWERED ### Given an indicated variable: S=180n-360 Solve it for n

Transformations of functions
ANSWERED 