Question

If the graph is reflected across the y-axis, what will be the equation of the new graph?

a) y=-3^-x+1

b) y=3^-x+1

c) y=-3^x-1

d) y=-3^x+1

Answer 1

Answer:

$\displaystyle b)y = { 3}^{ - x} + 1$

Step-by-step explanation:

we are given a exponential function

$\displaystyle y = {3}^{x} + 1$

we want to figure out the equation of the new graph reflected across the y-axis

remember that,

$\rm\displaystyle (x,y) \xrightarrow{ \text{ reflection over y - axis}}( - x,y)$

let y be $3^x+1$ so,

$\rm\displaystyle (x,y) \xrightarrow{ \text{ reflection over y - axis}}( - x, {3}^{ - x} + 1 )$

hence,

the equation of the new graph

$\displaystyle y = { 3}^{ - x} + 1$