Evaluating Functions

Practice Problems

Let \(f(x)=5x+3,\,\, g(x)=3x+5,\,\, h(x)=x^2+10\)

\(\textbf{1)}\) Find \(f(3)\)Link to Youtube Video with Solution to Question Number 1
\(\textbf{2)}\) Find \(g(4)\)
\(\textbf{3)}\) Find \(h(2)\)
\(\textbf{4)}\) Find \(f(-2)\)
\(\textbf{5)}\) Find \(g(0)\)




Let \(f(x)=x^2-1,\,\, g(x)=\sqrt{x+1},\,\, h(x)=\frac{24}{x+10}\)

\(\textbf{6)}\) Find \(f(8)\)
\(\textbf{7)}\) Find \(g(8)\)
\(\textbf{8)}\) Find \(h(2)\)
\(\textbf{9)}\) Find \(h(-4)\)
\(\textbf{10)}\) Find \(g(0)\)




Let \(f(x)=\sqrt{x-11},\,\, g(x)=x^2+3,\,\, h(x)=\frac{x}{6}\)

\(\textbf{11)}\) Find \(f(36)\)
\(\textbf{12)}\) Find \(h(6)\)
\(\textbf{13)}\) Find \(h(12)\)
\(\textbf{14)}\) Find \(g(2)\)
\(\textbf{15)}\) Find \(g(0)\)




Let \(f(x)=x^2-40,\,\, g(x)=\sqrt{2x+1},\,\, h(x)=\frac{2x+4}{x}\)

\(\textbf{16)}\) Find \(f(7)\)
\(\textbf{17)}\) Find \(g(4)\)
\(\textbf{18)}\) Find \(h(2)\)
\(\textbf{19)}\) Find \(h(4)\)
\(\textbf{20)}\) Find \(g(12)\)




Let \(f(x)=\sqrt{2x-1},\,\, g(x)=8x^2,\,\, h(x)=\frac{3x}{7}\)

\(\textbf{21)}\) Find \(f(5)\)
\(\textbf{22)}\) Find \(h(7)\)
\(\textbf{23)}\) Find \(g(1)\)
\(\textbf{24)}\) Find \(g(2)\)
\(\textbf{25)}\) Find \(g(0)\)




Use the table to evaluate

\(x\)
 \(0\) \(1\) \(2\) \(3\)
\(f(x)\)
 \(45\) \(12\) \(88\) \(33\)
\(g(x)\)
 \(67\) \(21\) \(24\) \(16\)
\(h(x)\)
 \(14\) \(30\) \(99\) \(22\)
\(\textbf{26)}\) Find \(f(1)\)
\(\textbf{27)}\) Find \(h(3)\)
\(\textbf{28)}\) Find \(g(2)\)
\(\textbf{29)}\) Find \(g(1)\)
\(\textbf{30)}\) Find \(f(0)\)




Use the graphs to evaluate.

Graph for questions 31-35

\(\textbf{31)}\) Find \(f(-1)\)
Link to Youtube Video with Solution to Question Number 31
\(\textbf{32)}\) Find \(f(1)\)
\(\textbf{33)}\) Find \(f(6)\)
\(\textbf{34)}\) Find \(f(4)\)
\(\textbf{35)}\) Find \(f(0)\)




Graph for questions 36-40

\(\textbf{36)}\) Find \(f(3)\)
\(\textbf{37)}\) Find \(f(2)\)
\(\textbf{38)}\) Find \(f(5)\)
\(\textbf{39)}\) Find \(f(-2)\)
\(\textbf{40)}\) Find \(f(4.5)\)


Challenge Problems

\(\textbf{41)}\) Find the value of x such that \(f(x)=g(x)\)
\(f(x)=3x+1, \text{ } g(x)=9-x\)


\(\textbf{42)}\) Find the value of x such that \(f(x)=g(x)\)
\(f(x)=x^2, \text{ } g(x)=x\)


\(\textbf{43)}\) Find the value of x such that \(f(x)=g(x)\)
\(f(x)=x^2-1, \text{ } g(x)=8\)



True or False?

\(\textbf{44)}\) All Functions are relations.
\(\textbf{45)}\) All relations are functions.



See Related Pages\(\)

\(\bullet\text{ Is it a function?}\)
\(\,\,\,\,\,\,\,\,(1,2),(2,4),(2,5),(5,8)\)
\(\bullet\text{ Is it linear?}\)
\(\,\,\,\,\,\,\,\,y=mx+b\)
\(\bullet\text{ Composite Functions}\)
\(\,\,\,\,\,\,\,\,(f\circ g)(x)=f(g(x))\)
\(\bullet\text{ Inverse Functions and Relations}\)
\(\,\,\,\,\,\,\,\,f^{-1}(x)=\frac{x+3}{2}\)
\(\bullet\text{ Operations of Functions}\)
\(\,\,\,\,\,\,\,\,(f+g)(3)=f(3)+g(3)\)


In Summary

Evaluating a function means to determine the value of the function at a specific input. To evaluate a function, you need to substitute the given input value for the variable in the function’s expression and simplify to find the output value.

Evaluating a function is an important concept in mathematics. It is useful for solving problems, making predictions, and understanding the behavior of functions meant to model real life situations.

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