Question

Consider the graph of the function f(x)=10^x

which statment describes a key feature of function g if g(x)=f(x+4)

Answer 1

Horizontal asymptote of y = 0

Explanation:

Given function:

`f(x)=10^x`

Given translation

`f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}`

Therefore,

`g(x)=f(x+4)=10^(x+4)`

So g(x) is f(x) translated 4 units left

As the curve has been translated horizontally, the horizontal asymptote will not change and so is still y = 0.

There is no x-intercept as the curve gets very close to, but never touches, the x-axis.

The y-intercept is when x = 0:

`\implies \textsf{y-intercept}=10^(0+4)=10^4=10000`

So the y-intercept of g(x) is (0, 10000)