Question

In Exercises 19–24, 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 exponential growth, which means the base of the exponential function is greater than 1, and the function increases as x increases. Step 2: Check the y-intercept of the graph. The y-intercept occurs when x = 0. From the graph, observe the value of the function at x = 0. Step 3: Compare the y-intercept to the given functions. For example, for f(x) = 3^x, the y-intercept is $$3^0 = 1. $$For g(x) = 3^(x-1), the y-intercept is $$3^{-1} = 1/3. $$For h(x) = 3^x - 1, the y-intercept is 1 - 1 = 0. Step 4: Look at the behavior of the graph for negative x-values. If the graph approaches zero but never touches the x-axis, it matches the behavior of 3^x or its transformations. If the graph is reflected or shifted, it will affect this behavior. Step 5: Based on the y-intercept and the shape, match the graph to the correct function from the options: f(x) = 3^x, g(x) = 3^(x-1), h(x) = 3^x - 1, f(x) = -3^x, G(x) = $$3^{-x}$$, or H(x) = $$-3^{-x}.$$

In Exercises 19–24, 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

Horizontal and Vertical Shifts

Reflections and Negative Exponents