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

Step-by-step explanation:

B. Is correct, the graph will never touch 0 if we shift the graphs horizontally,

Answer 2

Answer:

Horizontal asymptote of y = 0

Step-by-step 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)