Functions - SAT Math
Card 0 of 116
What is the definition of a function?
What is the definition of a function?
A relation in which each input has exactly one output.
A relation in which each input has exactly one output.
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What does $f(x)$ represent?
What does $f(x)$ represent?
The output (value of the function) when the input is $x$.
The output (value of the function) when the input is $x$.
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What is the domain of a function?
What is the domain of a function?
All possible input values ($x$) for which the function is defined.
All possible input values ($x$) for which the function is defined.
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What is the range of a function?
What is the range of a function?
All possible output values ($y$) of the function.
All possible output values ($y$) of the function.
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What does $f(a) = b$ mean?
What does $f(a) = b$ mean?
When $x = a$, the function’s output is $b$.
When $x = a$, the function’s output is $b$.
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What does $f(a + h) - f(a)$ represent?
What does $f(a + h) - f(a)$ represent?
The change in function value as $x$ increases by $h$.
The change in function value as $x$ increases by $h$.
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How do you test if a graph represents a function?
How do you test if a graph represents a function?
Use the vertical line test — if any vertical line crosses more than once, it’s not a function.
Use the vertical line test — if any vertical line crosses more than once, it’s not a function.
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What is the inverse of a function, conceptually?
What is the inverse of a function, conceptually?
It reverses the input–output pairs of the original function.
It reverses the input–output pairs of the original function.
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What does it mean for a function to be one-to-one?
What does it mean for a function to be one-to-one?
Each output is produced by exactly one input (passes the horizontal line test).
Each output is produced by exactly one input (passes the horizontal line test).
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Formula for a linear function.
Formula for a linear function.
$y = mx + b$.
$y = mx + b$.
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If $f(x) = 2x + 3$, find $f(4)$.
If $f(x) = 2x + 3$, find $f(4)$.
$f(4) = 2(4) + 3 = 11$.
$f(4) = 2(4) + 3 = 11$.
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If $f(x) = x^2 - 5x$, find $f(3)$.
If $f(x) = x^2 - 5x$, find $f(3)$.
$3^2 - 5(3) = 9 - 15 = -6$.
$3^2 - 5(3) = 9 - 15 = -6$.
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If $f(x) = 4x - 7$, find $x$ when $f(x) = 9$.
If $f(x) = 4x - 7$, find $x$ when $f(x) = 9$.
$9 = 4x - 7 \Rightarrow 4x = 16 \Rightarrow x = 4$.
$9 = 4x - 7 \Rightarrow 4x = 16 \Rightarrow x = 4$.
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If $f(x) = x^2 + 2x$, compute $f(a + 1)$.
If $f(x) = x^2 + 2x$, compute $f(a + 1)$.
$(a + 1)^2 + 2(a + 1) = a^2 + 4a + 3$.
$(a + 1)^2 + 2(a + 1) = a^2 + 4a + 3$.
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If $f(x) = 3x^2 - 2x + 5$, find $f(-2)$.
If $f(x) = 3x^2 - 2x + 5$, find $f(-2)$.
$3(4) - 2(-2) + 5 = 12 + 4 + 5 = 21$.
$3(4) - 2(-2) + 5 = 12 + 4 + 5 = 21$.
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Given $f(x) = x^2 - 9$, what is the domain?
Given $f(x) = x^2 - 9$, what is the domain?
All real numbers.
All real numbers.
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Given $f(x) = \frac{1}{x - 2}$, what is the domain?
Given $f(x) = \frac{1}{x - 2}$, what is the domain?
All real $x$ except $x = 2$.
All real $x$ except $x = 2$.
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Given $f(x) = \sqrt{x - 3}$, what is the domain?
Given $f(x) = \sqrt{x - 3}$, what is the domain?
$x \ge 3$.
$x \ge 3$.
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Given $f(x) = \sqrt{9 - x}$, what is the domain?
Given $f(x) = \sqrt{9 - x}$, what is the domain?
$x \le 9$.
$x \le 9$.
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If $f(x) = |x - 4|$, find $f(1)$.
If $f(x) = |x - 4|$, find $f(1)$.
$|1 - 4| = 3$.
$|1 - 4| = 3$.
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