# Transformation of functions questions and answers

Recent questions in Transformations of functions
Transformations of functions

### 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

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

Transformations of functions

### 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

### 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

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

Transformations of functions

### 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

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

Transformations of functions

### 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

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

Transformations of functions

### 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

### 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

### 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

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

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. $$\displaystyle{g{{\left({x}\right)}}}=−{\left({x}+{3}\right)}^{{3}}−{10}$$

Transformations of functions

### 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

### 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

### 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

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

Transformations of functions

### Given an indicated variable: S=180n-360 Solve it for n

Transformations of functions