Question

What type of transformation of the graph of f(x) = 5^x is the graph of f(x+1)?

Answer 1

The transformation of the graph is known as a horizontal shift.

What informs the horizontal shift of a graph?

The transformation of the graph of
`\(f(x) = 5^x\)` to
`\(f(x+1)\)` involves a horizontal shift to the left by 1 unit. When you replace
`\(x\)` with
`\(x + 1\)` in the function, it causes the entire graph to shift one unit to the left along the x-axis.

In general, if you have a function
`\(g(x) = f(x + a)\)`, where
`\(a\)` is a constant, it represents a horizontal shift of
`\(f(x)\)` to the left by
`\(a\)` units if
`\(a\)` is positive and to the right if
`\(a\)` is negative.

So, for
`\(f(x+1)\)`, the graph of
`\(5^x\)` is shifted to the left by 1 unit.