Using the graph estimate the following values.
- \(T(2) = \answer [tolerance=0.1]{-5.9}\)
- \(T(-6) = \answer [tolerance=0.1]{3.95}\)
- \(T(0) = \answer [tolerance=0.1]{3}\)
evaluating
Graphs
Let \(T\) be a function. Its graph is shown here.
Let \(f\) be a function. Its graph is shown here.
All of the values of \(T\) you determined above were real numbers.
- \(T(2)\) is a real number.
- \(T(-6)\) is a real number.
- \(T(0)\) is a real number.
Therefore, we could evaluate \(f\) at these numbers.
Using the graph estimate the following values.
- \(f(T(2)) = \answer [tolerance=0.1]{3}\)
- \(f(T(-6)) = \answer [tolerance=0.1]{4}\)
- \(f(T(0)) = \answer [tolerance=0.1]{2.75}\)
Use the graphs above to approximate the following expressions.
- \(f(T(8)) = \answer [tolerance=0.1]{2.37}\)
- \(T(f(0)) = \answer [tolerance=0.1]{-1.089}\)
- \(f(f(-4)) = \answer [tolerance=0.1]{0.9}\)
- \(T(T(3)) = \answer [tolerance=0.1]{3.036}\)
- \(f(T(-2.5)) = \answer [tolerance=0.1]{0.874}\)
- \(T(f(-1))+1 = \answer [tolerance=0.1]{-6.058}\)
- \(f(f(-6)) -5 = \answer [tolerance=0.1]{-2.255}\)
Formulas
Define the functions \(M\), \(N\), and \(P\) by the following formulas with their implied or natural domains.
\(\blacktriangleright \) \(M(t) = t^2 - 1\)
\(\blacktriangleright \) \(N(k) = \frac {k^2}{k + 1}\)
\(\blacktriangleright \) \(P(\theta ) = 3 \, \cos (\theta ) + 2\)
Use the formulas above to approximate the following expressions.
- \(N(M(1.7)) = \answer [tolerance=0.1]{1.236}\)
- \(M(P(0)) = \answer [tolerance=0.1]{24}\)
- \(N(N(8.3)) = \answer [tolerance=0.1]{6.526}\)
- \(P(P(-\pi )) = \answer [tolerance=0.1]{3.621}\)
- \(M(N(-2.5)) = \answer [tolerance=0.1]{16.361}\)
- \(N(M(-2.5)) = \answer [tolerance=0.1]{4.41}\)
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more examples can be found by following this link
More Examples of Pointwise Composition