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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Function notation is a special way to write functions that explicitly shows that $y$ is a function of $x.$ In other words, that $y$ depends on $x.$ Function notation is symbolically expressed as $f(x)=y,$
and read $f$ of $x$ equals $y.$

Remember that $x$ represents the inputs of the function and $y$ represents the outputs. Written in function notation, the function $y=5x−7$ becomes $f(x)=5x−7.$
Letters other than $f$ can be used to name a function. Additionally, function notation can be adjusted when the variable used to represent the input is not $x.$ For example, a function describing how the value, $V,$ of a car changes over time, $t,$ can be expressed as

Evaluating a function means finding the corresponding $x$- or $y$-value, given the other. When the function is given as a function rule, this is done by substituting the given value and solving for the remaining variable.

Given the function $f(x)=3x−4,$ evaluate the following statements. $f(3)andf(x)=23$

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$f(x)=3x−4$

Substitute$f(x)=23$

$23=3x−4$

AddEqn$LHS+4=RHS+4$

$27=3x$

DivEqn$LHS/3=RHS/3$

$9=x$

RearrangeEqnRearrange equation

$x=9$

Interpreting statements in function notation is sometimes necessary. To accomplish this, it's important to understand what the left- and right-hand sides of $f(x)=y$ mean. Suppose the following statement is given. $f(5)=25$ The left-hand side, $f(5),$ tells that the input of the function is $x=5.$ The right-hand side, $25,$ means that for the given input value, the output of the function is $25.$ Additionally, the statement $f(x)=25$ asks

$For which value ofxis the function’s value25? $Julianne and Douglas drive from California to New Mexico. During the first four hours of the trip, the function $d(t)=50t$ describes $d,$ the distance in miles they've driven in $t,$ the number of hours they've been traveling. Interpret the meaning of the following statements. $d(3.5)andd(t)=110$

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The function notation, $d(t),$ gives $d,$ the distance traveled in time $t.$ When we write $d(3.5),$ the time spent traveling is $3.5$ hours. Thus, the statement as a whole gives the distance traveled at $3.5$ hours.

Since $d(t)$ gives the distance traveled in time, $t,$ $d(t)=110$ asks the number of hours it takes to travel a distance of $110$ miles.

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