Respuesta :

Let's consider the principal function first:
[tex]f(x) = a^{x}[/tex]

For an exponential, we know that there is a horizontal asymptote at f(x) = 0. Thus, we know that [tex]f(x) = a^{x} > 0, x \in \mathbb{R}[/tex]

By moving the graph down 4 units, we have changed the range of the graph. For [tex]f(x) = a^{x}[/tex], there is a horizontal asymptote at y = 0, then there is a horizontal asymptote at y  = 4 for [tex]f(x) = a^{x} - 4[/tex]

Thus, we can conclude for any value of a, except for a = 1, we know that it will cross the x-axis.
apologiabiology
that means will we every get y=0
or f(x)=0

solve
0=a^x-4
not sure if
0=(a^x)-4 or
0=a^(x-4)

if it is the first one then
when a^x=4, then it will work (it will cross)

if it is the 2nd then it will never cross, just come very close (when x=- infinity, we get 1/(a^infinity) which approaches 0 but doesn't cross




if it is f(x)=aˣ-4 then it will cross
if it is f(x)=aˣ⁻⁴ then it will not cross

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