Function Notation

Function Notation

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Evaluate each of the following given the function definitions and input values. 

 $\left(a\right)\ f\left(x\right)=5x-2\$  
 $f\left(3\right)\ \ \ \ \ \ f\left(-2\right)$  

 $\left(b\right)\ g\left(x\right)=x^2+4$  
 $g\left(3\right)\ \ \ g\left(0\right)$  

Function Notation

 $y=f\left(x\right)$  
y= output
f=rule
x=input

Boiling water at 212 degrees Fahrenheit is left in a room that is at 65 degrees Fahrenheit and begins to cool. Temperature readings are taken each hour and are given in the table below. In this scenario, the temperature, T, is a function of the number of hours, h.

(a) Evaluate T (2) and T (6)

(b) For what value of h is

T(h) =76 ?

(c) Between what two consecutive hours will

T(h)= 100

The function y= f(x) is defined by the graph shown below. Answer the following questions based on this graph. 

(a) Evaluate f(-1) , f(1) , and f(5).

(b) Evaluate f(0) .

What special feature on a graph does f(0) always correspond to?

(c) What values of x solve the equation f(x)=0 ? What special features on a graph does the set of x-values that solve f(x)=0 correspond to? 

(d) Between what two consecutive integers does the largest solution to f(x)=3 lie?

Multiple Choice

For a function y=g(x) it is known that g(-2)= 7 . Which of the following points must lie on the graph of g(x)?

• (7,-2)

• (-2,7)

• (0,7)

• (-2,0)

 $h\left(t\right)=50\ -\ 16t^2$  

Physics students drop a ball from the top of a 50 foot high building and model its height as a function of time with the equation above . Using TABLES on your calculator, determine, to the nearest tenth of a second, when the ball hits the ground. 

Provide tabular outputs to support your answer.