Question

Write an equation for the graph​ below, which represents an exponential function f with base 2 or​ 3, translated​ and/or reflected.

Answer 1

Answer:

$f(x) = 2*2^x + 3$

Step-by-step explanation:

The model for an exponencial function is:

$f(x) = a*b^x + c$

'c' is the value of the asymptote, so we have c = 3.

To find the value of 'a', let's use the point (0,5):

$5 = a*b^0 + 3$

$5 = a*1 + 3$

$a = 2$

Now, to find the value of 'b', let's use the point (1, 7):

$7 = 2 * b^1 + 3$

$7 = 2b + 3$

$2b = 4$

$b = 2$

So our function is:

$f(x) = 2*2^x + 3$

Let's check if the point (-1, 4) is inside our function:

$4 = 2 * 2^{-1} + 3$

$4 = 1 + 3$

$4 = 4\ (correct)$