the graph of the function f(x)=x is transformed to form function g(x). the graphs of f and g are shown…

the graph of the function f(x)=x is transformed to form function g(x). the graphs of f and g are shown below. which of the following equations represents function g as a transformation of function f? g(x)=2f(x)+4 salsa sam was practicing taco juggling for the talent show, so cross off salsa sam and \wanted to impress their crush.\ g(x)=4f(x)+3 guac greg was experimenting with guacamole recipes, so cross off guac greg and \needed it for science.\ g(x)=\\frac{1}{3}f(x)-4 nacho nick was salsa dancing in the hallway, so cross off nacho nick and \wanted to impress their crush.\ g(x)=3f(x)+4 taco tina was grubbin near the cafe, so cross off taco tina and \needed a midnight snack.\

the graph of the function f(x)=x is transformed to form function g(x). the graphs of f and g are shown below. which of the following equations represents function g as a transformation of function f? g(x)=2f(x)+4 salsa sam was practicing taco juggling for the talent show, so cross off salsa sam and \wanted to impress their crush.\ g(x)=4f(x)+3 guac greg was experimenting with guacamole recipes, so cross off guac greg and \needed it for science.\ g(x)=\\frac{1}{3}f(x)-4 nacho nick was salsa dancing in the hallway, so cross off nacho nick and \wanted to impress their crush.\ g(x)=3f(x)+4 taco tina was grubbin near the cafe, so cross off taco tina and \needed a midnight snack.\

Answer

Explanation:

Step1: Recall slope - intercept form

The function $f(x)=x$ has a slope of 1 and y - intercept of 0. The general form of a linear transformation of $y = f(x)$ is $g(x)=af(x)+b$, where $a$ is the vertical stretch factor and $b$ is the vertical shift.

Step2: Find two points on $g(x)$

Two points on $g(x)$ are $(0,4)$ and $(2,10)$.

Step3: Calculate the slope of $g(x)$

The slope $m$ of $g(x)$ using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ for points $(x_1,y_1)=(0,4)$ and $(x_2,y_2)=(2,10)$ is $m=\frac{10 - 4}{2-0}=\frac{6}{2}=3$. Since $f(x)=x$, and $g(x)=af(x)+b$, the coefficient of $f(x)$ gives the slope change. Here $a = 3$.

Step4: Find the y - intercept of $g(x)$

The y - intercept of $g(x)$ is the value of $g(x)$ when $x = 0$. From the point $(0,4)$, the y - intercept $b = 4$. So $g(x)=3f(x)+4$.

Answer:

$g(x)=3f(x)+4$