Explain what happens to the graph y=4^x if you change it to 4^(x+3)+ 2
would it move 3 units to the right and 2 units upward-I'm thinking becaue youi're adding to the x??
almost. if
(y-k) = f(x-h)
that means that the graph is shifted h to the right, and k upward
So, in this problem,
f(x) = x^4
y-2 = f(x+3)
so the graph is shifted 3 to the left, and up 2.
oh okay-thank you
To understand what happens to the graph y = 4^x when you change it to 4^(x+3) + 2, you need to examine the effects of the changes in the equation.
1. Move 3 Units to the Right: Adding a number inside the parentheses of x, such as x+3, shifts the graph horizontally. In this case, adding 3 to x means the graph will move 3 units to the left, not right as you suggested.
2. Move 2 Units Upward: Any constant added outside the exponent affects the vertical position of the graph. Adding a constant to the entire equation, in this case, +2, means the graph will shift upward by 2 units.
Therefore, the correct explanation is that the graph y = 4^(x+3) + 2 will move 3 units to the left and 2 units upward compared to the original graph y = 4^x. Keep in mind that these transformations are applied in the order they are written in the equation.