Transformations

\(\begin{aligned}&\text{The function }f\text{ is defined by }f(x)=7x^{3}.\text{ In the }xy\text{-plane, the graph of }y=g(x)
\\&\text{is the result of shifting the graph of }y=f(x)\text{ down 2 units. Which equation }\\&\text{defines function }g?\end{aligned}\)

\(\begin{aligned}
&\text{In the }xy\text{-plane, the graph of the equation }y=9^{x}\text{ is translated 8 units down. What is}\\&\mathrm{an~equation~of~the~resulting~graph?}\end{aligned}\)

\(\text{The graph shown will be translated up 4 units. Which of the following will be the resulting graph?}\)

\(\begin{aligned}
&\text{The graph of the rational function }f\text{ is shown, where }y=f(x)\text{ and }x\geq0.\text{ Which of }\\&\text{the following is the graph of }y=f(x)+5,\text{ where }x\geq0?\end{aligned}\)

\(\text{The graph of }y=f(x)+1\text{ is shown. Which equation defines the function }f?\)

\(\text{The graph of }y=f(x)+2\text{ is shown. Which equation defines function }f?\)

\(\begin{aligned}&\text{The graph of }y=f(x)-1\text{ is shown. Which equation could define function }f?\end{aligned}\)

\(\begin{aligned}&\text{The graph of }y=f(x)+4\text{ is shown. Which equation defines function }f?\end{aligned}\)

\(\begin{aligned}
&\text{The rational function }f\text{ is defined by an equation in the form }f(x)={\frac{a}{x+b}},\\&\mathrm{where~}a\mathrm{~and~}b\text{ are constants}.\text{ The partial graph of }y=f(x)\text{ is shown. If}\\&g(x)=f(x+4),\text{which equation could define function }g?\end{aligned}\)

\(\begin{aligned}&\text{The graph of }y=f(x)+14\text{ is shown. Which equation defines function }f?\end{aligned}\)

\(\text{The graph of }y=f(x)-11\text{ is shown}.\)

\(\text{Which equation defines the linear function }f?\)

\(\text{The graph of }y=f(x)\text{ is shown. What is the }y\text{-intercept of the graph of }y=f(x)+13?\)

\(\begin{aligned}
&\text{The graph of the linear function }y=f(x)-19\text{ is shown. If }c\text{ and }d\text{ are positive constants,}\\&\text{which equation could define }f?\end{aligned}\)

\(\begin{aligned}
&\text{The graph of the linear function }y=f(x)+11\text{ is shown. If }c\text{ and }d\text{ are positive constants,}\\&\text{which equation could define }f?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~g(x)=3(16x-17)\\
&\text{What is the }y\text{-coordinate of the }y\text{-intercept}\text{ of the graph of }y=g(x)-5\\&\text{in the }xy\text{-plane?}\end{aligned}\)

\(\begin{aligned}&\text{The function }f\text{ is defined by }f(x)=(x-6)(x-2)(x+6).\text{ In the }xy\text{-plane, the}\\&\text{graph of }y=g(x)\text{ is the result of translating the graph of }y=f(x)\text{ up }4\text{units. }\\&\text{What is the value of }g(0)?\end{aligned}\)

\(\begin{aligned}&\text{The function }f\text{ is defined by }f(x)=(x-9)(x-6)(x-5).\text{ In the }xy\text{-plane, the}\\&\text{graph of }y=g(x)\text{ is the result of translating the graph of }y=f(x)\text{ up }4\text{units. }\\&\text{What is the value of }g(0)?\end{aligned}\)

\(\begin{aligned}
&\text{The graph of 9}x-10y=19\text{ is translated down 4 units in the }xy\text{-plane. What is the }\\&x\text{-coordinate of the }x\text{-intercept of the resulting graph?}\end{aligned}\)

\(\begin{aligned}
&\text{For the linear function }f\text{, the table shows three values of }x\text{ and their corresponding}\\&\text{values of }f(x).\text{ If }h(x)=f(x)-13,\text{ which equation defines }h?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline x&y\\\hline18&130\\\hline23&160\\\hline26&178\\\hline\end{array}\\\\
&\text{For line }h,\text{ the table shows three values of }x\text{ and their corresponding values of }y.\\&\text{Line }k \text{ is the result of translating line }h\mathrm{~down~}5\text{ units in the }xy\text{-plane. What is the}\\&x\text{-intercept of line }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline x&y\\\hline20&-20\\\hline24&12\\\hline28&-20\\\hline\end{array}\\\\
&\text{The table shows three values of }x\text{ and their corresponding values of }y,\text{ where }y=f(x)+6\\&\text{ and }f\text{ is a quadratic function. What is the }y\text{-coordinate of the }y\text{-intercept of the graph of}\\&y=f(x)\text{ in the }xy\text{-plane?}\end{aligned}\)

\(\begin{aligned}
&\text{Function }f\text{ is defined by }f(x)=(x+6)(x+5)(x+1).\text{ Function }g\text{ is defined by }g(x)=f(x-1).\\
&\text{The graph of }y=g(x)\text{ in the }xy\text{-plane has }x\text{-intercepts at }(a,0),(b,0)\text{, and }(c,0),\text{where }a,b\\
&\mathrm{and~}c\text{ are distinct constants. What is the value of }a+b+c?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=(x+6)(x+5)(x-4)\\\\&\text{The function }f\text{ is given. Which table of values represents }y=f(x)-3?\end{aligned}\)

\(\begin{aligned}&\text{The graph of }y=f(x)-k\text{ is shown in the }xy\text{-plane. If }k,a,\mathrm{~and~}b\text{ are positive constants},\\&\text{which equation could define }f?\end{aligned}\)