Question

Which ordered pairs lie on the graph of the exponential function f(x)=2^(x+4)−8?

Answer 1

Given the function

$f(x)=2^{(x+4)}-8$

Consider the point (2, 56) i.e. when x = 2

$f(x)=2^{2+4}-8 \\ \\ =2^6-8=64-8 \\ \\ =56$

Therefore, point (2, 56) lie on the graph of the given exponential function.

Consider the point (-2, -4) i.e. when x = -2

$f(x)=2^{-2+4}-8 \\ \\ =2^2-8=4-8 \\ \\ =-4$

Therefore, point (-2, -4) lie on the graph of the given exponential function.

Consider the point (8, 0) i.e. when x = 8

$f(x)=2^{8+4}-8 \\ \\ =2^{12}-8=4,096-8 \\ \\ =4,088$

Therefore, point (8, 0) does not lie on the graph of the given exponential function.

Consider the point (24, 1) i.e. when x = 24

$f(x)=2^{24+4}-8 \\ \\ =2^{28}-8=268,435,456-8 \\ \\ =-268,435,448$

Therefore, point (24, 1) does not lie on the graph of the given exponential function.