Question

In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = 3x and g(x) = -3x

Accepted Answer

Identify the base function and its transformation: The base function is $$f(x) = 3^x$$, which is an exponential function with base 3. Understand the transformation from $$f(x) to$$ $$g(x)$$: The function $$g(x) = -3^x is $$obtained by reflecting the graph of $$f(x)$$ across the x-axis because of the negative sign in front. Graph $$f(x) = 3^x$$: Plot points for several values of $$x (e.g$$., $$x = -2, -1, 0, 1, 2) to $$see the exponential growth. Note that $$f(x)$$ approaches 0 as $$x$$ approaches negative infinity but never touches the x-axis. Graph $$g(x) = -3^x$$: Use the reflection transformation on the points of $$f(x) by $$multiplying the $$y-$$values by -1. This flips the graph over the x-axis, so it approaches 0 from below as $$x$$ approaches negative infinity. Determine the asymptotes, domain, and range: Both functions have a horizontal asymptote at $$y=0. $$The domain for both is all real numbers, $$(-\infty, \infty). $$The range of $$f(x) is$$ $$(0, \infty)$$, and the range of $$g(x) is$$ $$(-\infty, 0).$$

In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = 3^x and g(x) = -3^x

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Exponential Functions and Their Graphs

Transformations of Functions

Asymptotes, Domain, and Range