let ( f(x)=4^{x}-1 ) draw the graph of ( f ) using the coordinate grid below.
let ( f(x)=4^{x}-1 ) draw the graph of ( f ) using the coordinate grid below.
Answer
Explanation:
Step1: Find some points on the function
When (x = 0), (f(0)=4^{0}-1=1 - 1=0). When (x = 1), (f(1)=4^{1}-1=4 - 1 = 3). When (x = 2), (f(2)=4^{2}-1=16 - 1=15). When (x=-1), (f(-1)=4^{-1}-1=\frac{1}{4}-1=-\frac{3}{4}).
Step2: Plot the points and draw the curve
Plot the points ((0,0)), ((1,3)), ((2,15)), ((-1,-\frac{3}{4})) on the coordinate grid. Then, since (y = 4^{x}-1) is an exponential function (a transformation of (y = 4^{x}) shifted down by 1 unit), connect the points with a smooth curve. The general shape of (y = a^{x}) ((a>1)) is an increasing curve. As (x\rightarrow-\infty), (y = 4^{x}-1\rightarrow - 1) (horizontal asymptote (y=-1)), and as (x\rightarrow+\infty), (y = 4^{x}-1\rightarrow+\infty).
Answer:
Plot the points ((0,0)), ((1,3)), ((2,15)), ((-1,-\frac{3}{4})) and draw an increasing curve approaching the horizontal asymptote (y = - 1) as (x\rightarrow-\infty) and going to (+\infty) as (x\rightarrow+\infty) on the given coordinate grid.