Domain and Range help
- Thread starter xcarbonx
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mmm4444bot
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Hi xcarbonx:
Are you familiar with the domain and range of the "basic" functions?
For examples:
y = b^x [basic exponential function with base b]
y = ln(x) [basic logarithmic function with base e]
It's more difficult to answer these types of exercises, if we don't know the shapes and positions of these basic graphs.
Are you familiar with shifted graphs?
The graph of f(x) = 3^(x + 2) - 4 is a horizontally- and vertically-shifted graph of y = 3^x.
In other words, if you know the domain and range of y = 3^x, and you understand the shifts involved to obtain function f, then the domain and range of f become apparent.
Likewise, if you know the domain and range of y = ln(x), and you understand the shift to become g(x) = ln(x + 3), then the domain and range of function g become clear.
If you've forgotten the domains and ranges of the basic graphs, or you've forgotten the types of changes that lead to horizontal and vertical shifts, then you need to review before trying to answer exercises like these two.
If you need more help, please be more specific about WHY you are uncertain. I'm not sure what it means to understand domain and range "somewhat".
Cheers ~ Mark
Are you familiar with the domain and range of the "basic" functions?
For examples:
y = b^x [basic exponential function with base b]
y = ln(x) [basic logarithmic function with base e]
It's more difficult to answer these types of exercises, if we don't know the shapes and positions of these basic graphs.
Are you familiar with shifted graphs?
The graph of f(x) = 3^(x + 2) - 4 is a horizontally- and vertically-shifted graph of y = 3^x.
In other words, if you know the domain and range of y = 3^x, and you understand the shifts involved to obtain function f, then the domain and range of f become apparent.
Likewise, if you know the domain and range of y = ln(x), and you understand the shift to become g(x) = ln(x + 3), then the domain and range of function g become clear.
If you've forgotten the domains and ranges of the basic graphs, or you've forgotten the types of changes that lead to horizontal and vertical shifts, then you need to review before trying to answer exercises like these two.
If you need more help, please be more specific about WHY you are uncertain. I'm not sure what it means to understand domain and range "somewhat".
Cheers ~ Mark