Answer:
[tex]f(x)=2^x-3[/tex]
Step-by-step explanation:
This is an exponential function, in these kind of function the independent variable appears in the exponent and its base is a constant. Its expression is given by:
[tex]f(x)=a^x\\\\a\neq \pm1[/tex]
If [tex]a>0[/tex] the exponential function is an increasing function, and if [tex]a<0[/tex] the exponential function is a decreasing function, on the other hand, exponential functions always pass through the points (0, 1) and (1, a), because:
[tex]f(0)=a^0=1\\f(1)=a^1=a[/tex]
Considering the previous information, you can conclude:
[tex]a>0[/tex]
Because from the graph, you can note that it is an increasing function.
Therefore, from the options:
[tex]a=2[/tex]
On the other hand the graph pass through the point (0, -2), this means that the graph was translate h units down.
[tex]f(x)=2^x-h[/tex]
So, let's find h:
[tex]f(0)=-2=2^0 - h\\\\f(0)=-2=1-h[/tex]
Solving for h:
[tex]h=3[/tex]
Hence, the equation represented by the graph is:
[tex]f(x)=2^x-3[/tex]
I attached you the graph of this function, so you can corroborate the answer easily.
