Question

The graph of an exponential function is given. Select the function for each graph from the following options: ﻿f(x)=3x,g(x)=3x−1,h(x)=3x−1,f(x)=−3x,G(x)=3−x,H(x)=−3−x.f(x) = 3^x, \quad g(x) = $$3^{x-1}$$, \quad h(x) = 3^x - 1, \
f(x) = -3^x, \quad G(x) = $$3^{-x}$$, \quad H(x) = $$-3^{-x}.
f(x)=3x$$,g(x)=3x−1,h(x)=3x−1,f(x)=−3x,G(x)=3−x,H(x)=−3−x.

Accepted Answer

Step 1: Identify the general shape of the graph. The graph shows a decreasing curve that approaches zero as x increases, which is characteristic of an exponential decay function. Step 2: Recall the given function options: $$f(x) = 3^x$$, $$g(x) = 3$$^{x-1}$$, h(x) = 3^x - 1$, f(x) = -3^x$, G(x$$) = $$3^{-x}$$, and $$H(x) = -3$$^{-x}$$. Notice that functions with 3^x$ grow exponentially, while those with 3$$^{-x}$$ decay exponentially. Step 3: Since the graph is decreasing and approaches zero as x increases, focus on functions with negative exponents, such as G(x$$) = $$3^{-x}$$ and $$H(x) = -3$$^{-x}$$. Step 4: Check the sign of the function values. The graph is above the x-axis (positive values), so the function is positive. This rules out H(x$$) = $$-3^{-x}$$, which would be negative. Step 5: Verify the y-intercept by substituting $$x=0$$ into $$G(x) = 3$$^{-x}$$. This gives G(0$$) = $$3^0 = 1$. Compare this with the graph's y-intercept to confirm the match.

The graph of an exponential function is given. Select the function for each graph from the following options:
$f(x) = 3^x, \(\quad\) g(x) = 3^{x-1}, \(\quad\) h(x) = 3^x - 1, \(\f\)(x) = -3^x, \(\quad\) G(x) = 3^{-x}, \(\quad\) H(x) = -3^{-x}.$

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Exponential Functions and Their Graphs

Transformations of Exponential Functions

Identifying Decreasing vs. Increasing Exponential Functions