standard 10 homework\nscore: 13/24 answered: 11/20\nquestion 12\ndraw the graph of $f(x)=5^{x + 2}$\nclear…

Explanation:

Step1: Find some points

Let's choose some values of (x) to calculate (y = f(x)=5^{x + 2}). When (x=-2), (y = 5^{-2+2}=5^{0}=1). When (x=-1), (y = 5^{-1 + 2}=5^{1}=5). When (x = 0), (y=5^{0+2}=25).

Step2: Analyze the function properties

The general form of an exponential function is (y = a^{x + h}), where (a = 5>1). The function (y = 5^{x+2}) is an exponential growth function. The graph of (y = 5^{x}) is shifted (2) units to the left to get the graph of (y = 5^{x + 2}).

Step3: Plot the points and draw the graph

Plot the points ((-2,1)), ((-1,5)), ((0,25)) on the coordinate plane. Then, since it is an exponential growth function ((a>1)), as (x\to-\infty), (y\to0) (the (x) - axis is a horizontal asymptote (y = 0)), and as (x\to+\infty), (y\to+\infty). Connect the points with a smooth curve.

Answer:

Plot the points ((-2,1)), ((-1,5)), ((0,25)) and draw a smooth exponential growth curve approaching the (x) - axis as (x\to-\infty) and increasing without bound as (x\to+\infty).