Function Notation and Evaluation - Algebra
Card 1 of 30
Find $h(0)$ if $h(x)=5-3x$.
Find $h(0)$ if $h(x)=5-3x$.
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$h(0)=5$. Substitute $x=0$: $h(0)=5-3(0)=5$.
$h(0)=5$. Substitute $x=0$: $h(0)=5-3(0)=5$.
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Identify whether $f(2)$ is defined if $f(x)=\frac{1}{x-2}$.
Identify whether $f(2)$ is defined if $f(x)=\frac{1}{x-2}$.
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$f(2)$ is undefined. Division by zero occurs when $x=2$.
$f(2)$ is undefined. Division by zero occurs when $x=2$.
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Find $p(1)$ if $p(x)=3x^2+2x$.
Find $p(1)$ if $p(x)=3x^2+2x$.
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$p(1)=5$. Substitute $x=1$: $p(1)=3(1)^2+2(1)=5$.
$p(1)=5$. Substitute $x=1$: $p(1)=3(1)^2+2(1)=5$.
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Find $f(-3)$ if $f(x)=x^2-1$.
Find $f(-3)$ if $f(x)=x^2-1$.
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$f(-3)=8$. Substitute $x=-3$: $f(-3)=(-3)^2-1=8$.
$f(-3)=8$. Substitute $x=-3$: $f(-3)=(-3)^2-1=8$.
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Find $f(4)$ if $f(x)=2x+5$.
Find $f(4)$ if $f(x)=2x+5$.
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$f(4)=13$. Substitute $x=4$: $f(4)=2(4)+5=13$.
$f(4)=13$. Substitute $x=4$: $f(4)=2(4)+5=13$.
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Find $q(-2)$ if $q(x)=x^2+4x+1$.
Find $q(-2)$ if $q(x)=x^2+4x+1$.
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$q(-2)=-3$. Substitute $x=-2$: $q(-2)=(-2)^2+4(-2)+1=-3$.
$q(-2)=-3$. Substitute $x=-2$: $q(-2)=(-2)^2+4(-2)+1=-3$.
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Find $g(2)$ if $g(x)=\frac{1}{2}x-4$.
Find $g(2)$ if $g(x)=\frac{1}{2}x-4$.
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$g(2)=-3$. Substitute $x=2$: $g(2)=\frac{1}{2}(2)-4=-3$.
$g(2)=-3$. Substitute $x=2$: $g(2)=\frac{1}{2}(2)-4=-3$.
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Interpret $d(2.5)=150$ if $d(t)$ is distance in miles after $t$ hours.
Interpret $d(2.5)=150$ if $d(t)$ is distance in miles after $t$ hours.
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After $2.5$ hours, the distance traveled is $150$ miles. Function describes distance as function of time.
After $2.5$ hours, the distance traveled is $150$ miles. Function describes distance as function of time.
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What does the notation $f(x)$ represent in function notation?
What does the notation $f(x)$ represent in function notation?
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$f(x)$ is the output value of function $f$ for input $x$. Function notation shows the input-output relationship.
$f(x)$ is the output value of function $f$ for input $x$. Function notation shows the input-output relationship.
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What is the meaning of the statement $f(3)=7$?
What is the meaning of the statement $f(3)=7$?
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When $x=3$, the function output is $7$. Substitute $x=3$ into the function to get output $7$.
When $x=3$, the function output is $7$. Substitute $x=3$ into the function to get output $7$.
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What is the meaning of the statement $f(a)=b$?
What is the meaning of the statement $f(a)=b$?
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When $x=a$, the function output is $b$. General form showing input $a$ produces output $b$.
When $x=a$, the function output is $b$. General form showing input $a$ produces output $b$.
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What is the domain of a function in words?
What is the domain of a function in words?
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The set of all allowable input values. Only these values can be substituted into the function.
The set of all allowable input values. Only these values can be substituted into the function.
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What is the range of a function in words?
What is the range of a function in words?
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The set of all possible output values. All values the function can produce as outputs.
The set of all possible output values. All values the function can produce as outputs.
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What is the standard notation for the output variable of $f(x)$?
What is the standard notation for the output variable of $f(x)$?
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$y=f(x)$. Standard way to represent function output.
$y=f(x)$. Standard way to represent function output.
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What does it mean if an input $x$ is not in the domain of $f$?
What does it mean if an input $x$ is not in the domain of $f$?
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$f(x)$ is undefined for that input. The function cannot be evaluated at that input.
$f(x)$ is undefined for that input. The function cannot be evaluated at that input.
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What is the difference between $f(x)$ and $f\cdot x$?
What is the difference between $f(x)$ and $f\cdot x$?
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$f(x)$ is a function value; $f\cdot x$ is multiplication. Parentheses indicate function evaluation, not multiplication.
$f(x)$ is a function value; $f\cdot x$ is multiplication. Parentheses indicate function evaluation, not multiplication.
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What is the difference between $f(x)$ and $f,x$ in algebra?
What is the difference between $f(x)$ and $f,x$ in algebra?
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$f(x)$ is a function value; $f,x$ is multiplication. Parentheses indicate function evaluation, not multiplication.
$f(x)$ is a function value; $f,x$ is multiplication. Parentheses indicate function evaluation, not multiplication.
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What does $f(x+h)$ mean in function notation?
What does $f(x+h)$ mean in function notation?
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The output when the input is $x+h$. Substitute the entire expression $(x+h)$ for $x$.
The output when the input is $x+h$. Substitute the entire expression $(x+h)$ for $x$.
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What does $f(x)-f(a)$ represent?
What does $f(x)-f(a)$ represent?
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The difference between outputs at inputs $x$ and $a$. Shows the change in function values between inputs.
The difference between outputs at inputs $x$ and $a$. Shows the change in function values between inputs.
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What does the statement $f(x)=0$ ask you to find?
What does the statement $f(x)=0$ ask you to find?
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All inputs $x$ that make the output equal to $0$. Find the zeros or roots of the function.
All inputs $x$ that make the output equal to $0$. Find the zeros or roots of the function.
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What does the statement $f(x)>0$ describe?
What does the statement $f(x)>0$ describe?
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Inputs $x$ where the function output is positive. The function is above the $x$-axis at these inputs.
Inputs $x$ where the function output is positive. The function is above the $x$-axis at these inputs.
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Find the domain of $f(x)=\sqrt{x+4}$ in inequality form.
Find the domain of $f(x)=\sqrt{x+4}$ in inequality form.
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$x\ge -4$. Square root requires $x+4\ge 0$.
$x\ge -4$. Square root requires $x+4\ge 0$.
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Find the domain of $f(x)=\frac{x+1}{x-7}$ in restriction form.
Find the domain of $f(x)=\frac{x+1}{x-7}$ in restriction form.
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All real $x$ such that $x\neq 7$. Denominator cannot equal zero.
All real $x$ such that $x\neq 7$. Denominator cannot equal zero.
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Find the domain of $f(x)=\frac{1}{(x-1)(x+2)}$ in restriction form.
Find the domain of $f(x)=\frac{1}{(x-1)(x+2)}$ in restriction form.
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All real $x$ such that $x\neq 1$ and $x\neq -2$. Both factors in denominator cannot equal zero.
All real $x$ such that $x\neq 1$ and $x\neq -2$. Both factors in denominator cannot equal zero.
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Interpret $C(10)=25$ if $C(d)$ is the cost in dollars for $d$ miles.
Interpret $C(10)=25$ if $C(d)$ is the cost in dollars for $d$ miles.
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A $10$-mile trip costs $25$ dollars. Function notation describes real-world relationships.
A $10$-mile trip costs $25$ dollars. Function notation describes real-world relationships.
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Interpret $T(3)=68$ if $T(h)$ is temperature after $h$ hours.
Interpret $T(3)=68$ if $T(h)$ is temperature after $h$ hours.
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After $3$ hours, the temperature is $68$ degrees. Function value represents temperature at specific time.
After $3$ hours, the temperature is $68$ degrees. Function value represents temperature at specific time.
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Interpret $P(5)=1200$ if $P(t)$ is population after $t$ years.
Interpret $P(5)=1200$ if $P(t)$ is population after $t$ years.
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After $5$ years, the population is $1200$. Function output shows population at given time.
After $5$ years, the population is $1200$. Function output shows population at given time.
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What does $f(0)$ represent on the graph of $y=f(x)$?
What does $f(0)$ represent on the graph of $y=f(x)$?
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The $y$-intercept value. When $x=0$, output gives $y$-intercept.
The $y$-intercept value. When $x=0$, output gives $y$-intercept.
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What point corresponds to $f(a)=b$ on the graph of $y=f(x)$?
What point corresponds to $f(a)=b$ on the graph of $y=f(x)$?
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The point $(a,b)$. Function notation corresponds to coordinate pairs.
The point $(a,b)$. Function notation corresponds to coordinate pairs.
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Identify the input and output in the ordered pair $(x,f(x))$.
Identify the input and output in the ordered pair $(x,f(x))$.
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Input is $x$; output is $f(x)$. First coordinate is input, second is output.
Input is $x$; output is $f(x)$. First coordinate is input, second is output.
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