A function g is given. Identify the parent function. Then use the steps for graphing multiple
transformations of functions to list, in order, the transformations applied to the parent function to obtain
the graph of g.
-$$g ( x ) = \frac { 1 } { 5 } ( x + 1.3 ) ^ { 2 } - 2.5$$
A) Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the right $1.3$ units, shrink the graph vertically by a factor of $\frac { 1 } { 5 }$, and shift the graph upward by $2.5$ units.

B) Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the left $1.3$ units, strech the graph vertically by a factor of 5 , and shift the graph downward by $2.5$ units.

C) Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the right $1.3$ units, stretch the graph vertically by a factor of 5 , and shift the graph upward by $2.5$ units.

D) Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the left $1.3$ units, shrink the graph vertically by a factor of $\frac { 1 } { 5 }$, and shift the graph downward by $2.5$ units.

Question

A function g is given. Identify the parent function. Then use the steps for graphing multiple
transformations of functions to list, in order, the transformations applied to the parent function to obtain
the graph of g.
-$$g ( x ) = \frac { 1 } { 5 } ( x + 1.3 ) ^ { 2 } - 2.5$$
A) Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the right $1.3$ units, shrink the graph vertically by a factor of $\frac { 1 } { 5 }$, and shift the graph upward by $2.5$ units.

B) Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the left $1.3$ units, strech the graph vertically by a factor of 5 , and shift the graph downward by $2.5$ units.

C) Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the right $1.3$ units, stretch the graph vertically by a factor of 5 , and shift the graph upward by $2.5$ units.

D) Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the left $1.3$ units, shrink the graph vertically by a factor of $\frac { 1 } { 5 }$, and shift the graph downward by $2.5$ units.

Quizplus · Accepted Answer

The parent function is $f(x) = x^2$. The transformation involves shifting to the left by $1.3$ units (due to $x+1.3$), shrinking vertically by a factor of $\frac{1}{5}$ (due to the coefficient $\frac{1}{5}$), and shifting downward by $2.5$ units (due to $-2.5$).

A Function G Is Given g(x)=15(x+1.3)2−2.5g ( x ) = \frac { 1 } { 5 } ( x + 1.3 ) ^ { 2 } - 2.5g(x)=51​(x+1.3)2−2.5

A Function G Is Given $g ( x ) = \frac { 1 } { 5 } ( x + 1.3 ) ^ { 2 } - 2.5$