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

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

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`