Read Inverses from Graphs or Tables - Algebra 2
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What is $f^{-1}(13)$ if the graph of $f$ includes $(0,13)$?
What is $f^{-1}(13)$ if the graph of $f$ includes $(0,13)$?
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$f^{-1}(13)=0$. Read the $x$-coordinate where the graph has $y=13$.
$f^{-1}(13)=0$. Read the $x$-coordinate where the graph has $y=13$.
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What is $f^{-1}(-2)$ if the graph of $f$ includes $(9,-2)$?
What is $f^{-1}(-2)$ if the graph of $f$ includes $(9,-2)$?
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$f^{-1}(-2)=9$. Read the $x$-coordinate where the graph has $y=-2$.
$f^{-1}(-2)=9$. Read the $x$-coordinate where the graph has $y=-2$.
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What happens to the domain and range when passing from $f$ to $f^{-1}$?
What happens to the domain and range when passing from $f$ to $f^{-1}$?
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Domain and range swap between $f$ and $f^{-1}$. The input set of one becomes the output set of the other.
Domain and range swap between $f$ and $f^{-1}$. The input set of one becomes the output set of the other.
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What is $f^{-1}(7)$ if a table shows $f(2)=7$?
What is $f^{-1}(7)$ if a table shows $f(2)=7$?
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$f^{-1}(7)=2$. The inverse reverses the input-output pair $(2,7)$.
$f^{-1}(7)=2$. The inverse reverses the input-output pair $(2,7)$.
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What equation states the composition identity for inverses using $f^{-1}(f(x))$?
What equation states the composition identity for inverses using $f^{-1}(f(x))$?
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$f^{-1}(f(x))=x$ (for $x$ in the domain of $f$). Composing an inverse with its function yields the identity.
$f^{-1}(f(x))=x$ (for $x$ in the domain of $f$). Composing an inverse with its function yields the identity.
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What graph test checks whether a function is one-to-one?
What graph test checks whether a function is one-to-one?
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The horizontal line test. No horizontal line intersects the graph more than once.
The horizontal line test. No horizontal line intersects the graph more than once.
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Identify the meaning of the statement $f^{-1}(y)=x$ in terms of $f$.
Identify the meaning of the statement $f^{-1}(y)=x$ in terms of $f$.
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It means $f(x)=y$. The inverse notation shows which input produces output $y$.
It means $f(x)=y$. The inverse notation shows which input produces output $y$.
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What is the $y$-intercept of $f^{-1}$ if the $x$-intercept of $f$ is $(c,0)$?
What is the $y$-intercept of $f^{-1}$ if the $x$-intercept of $f$ is $(c,0)$?
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The $y$-intercept of $f^{-1}$ is $(0,c)$. Intercepts swap coordinates when finding the inverse.
The $y$-intercept of $f^{-1}$ is $(0,c)$. Intercepts swap coordinates when finding the inverse.
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What is $f^{-1}(0)$ if a table shows $f(-4)=0$?
What is $f^{-1}(0)$ if a table shows $f(-4)=0$?
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$f^{-1}(0)=-4$. The inverse reverses the input-output pair $(-4,0)$.
$f^{-1}(0)=-4$. The inverse reverses the input-output pair $(-4,0)$.
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What is $f^{-1}(12)$ if a table shows $f(9)=12$?
What is $f^{-1}(12)$ if a table shows $f(9)=12$?
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$f^{-1}(12)=9$. The inverse reverses the input-output pair $(9,12)$.
$f^{-1}(12)=9$. The inverse reverses the input-output pair $(9,12)$.
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What point lies on $f^{-1}$ if the point $(0,-7)$ lies on $f$?
What point lies on $f^{-1}$ if the point $(0,-7)$ lies on $f$?
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$(-7,0)$ lies on $f^{-1}$. Inverse functions swap the coordinates of points.
$(-7,0)$ lies on $f^{-1}$. Inverse functions swap the coordinates of points.
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What is $f^{-1}(2)$ if a table shows $f(-1)=2$?
What is $f^{-1}(2)$ if a table shows $f(-1)=2$?
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$f^{-1}(2)=-1$. The inverse reverses the input-output pair $(-1,2)$.
$f^{-1}(2)=-1$. The inverse reverses the input-output pair $(-1,2)$.
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What is $f^{-1}(10)$ if a table shows $f(3)=10$?
What is $f^{-1}(10)$ if a table shows $f(3)=10$?
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$f^{-1}(10)=3$. The inverse reverses the input-output pair $(3,10)$.
$f^{-1}(10)=3$. The inverse reverses the input-output pair $(3,10)$.
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Identify $f^{-1}(0)$ if a graph of $f$ crosses the $x$-axis at $(7,0)$.
Identify $f^{-1}(0)$ if a graph of $f$ crosses the $x$-axis at $(7,0)$.
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$f^{-1}(0)=7$. The $x$-intercept shows where $f(x)=0$.
$f^{-1}(0)=7$. The $x$-intercept shows where $f(x)=0$.
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Identify $f^{-1}(0)$ if a graph of $f$ crosses the $y$-axis at $(0,7)$.
Identify $f^{-1}(0)$ if a graph of $f$ crosses the $y$-axis at $(0,7)$.
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$f^{-1}(0)$ is not determined from $(0,7)$ alone. The $y$-intercept alone doesn't show where $f(x)=0$.
$f^{-1}(0)$ is not determined from $(0,7)$ alone. The $y$-intercept alone doesn't show where $f(x)=0$.
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What is $f^{-1}(x)$ at $x=4$ if the table shows $f(1)=4$?
What is $f^{-1}(x)$ at $x=4$ if the table shows $f(1)=4$?
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$f^{-1}(4)=1$. The inverse reverses the input-output pair $(1,4)$.
$f^{-1}(4)=1$. The inverse reverses the input-output pair $(1,4)$.
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What is $f^{-1}(x)$ at $x=-8$ if the table shows $f(0)=-8$?
What is $f^{-1}(x)$ at $x=-8$ if the table shows $f(0)=-8$?
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$f^{-1}(-8)=0$. The inverse reverses the input-output pair $(0,-8)$.
$f^{-1}(-8)=0$. The inverse reverses the input-output pair $(0,-8)$.
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What is the value of $f^{-1}(b)$ if the graph shows the point $(b,a)$ on $f^{-1}$?
What is the value of $f^{-1}(b)$ if the graph shows the point $(b,a)$ on $f^{-1}$?
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$f^{-1}(b)=a$. Reading coordinates directly from the inverse graph.
$f^{-1}(b)=a$. Reading coordinates directly from the inverse graph.
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What is the value of $f(a)$ if the graph shows the point $(a,b)$ on $f$?
What is the value of $f(a)$ if the graph shows the point $(a,b)$ on $f$?
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$f(a)=b$. Reading coordinates directly from the function graph.
$f(a)=b$. Reading coordinates directly from the function graph.
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Which ordered pair on $f$ corresponds to the point $(2,9)$ on $f^{-1}$?
Which ordered pair on $f$ corresponds to the point $(2,9)$ on $f^{-1}$?
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$(9,2)$ on $f$. Inverse functions swap coordinates of corresponding points.
$(9,2)$ on $f$. Inverse functions swap coordinates of corresponding points.
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Which ordered pair on $f^{-1}$ corresponds to the point $(-3,11)$ on $f$?
Which ordered pair on $f^{-1}$ corresponds to the point $(-3,11)$ on $f$?
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$(11,-3)$ on $f^{-1}$. Inverse functions swap coordinates of corresponding points.
$(11,-3)$ on $f^{-1}$. Inverse functions swap coordinates of corresponding points.
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Identify the point on $f^{-1}$ that corresponds to the $y$-intercept $(0,c)$ of $f$.
Identify the point on $f^{-1}$ that corresponds to the $y$-intercept $(0,c)$ of $f$.
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The point $(c,0)$ on $f^{-1}$. The $y$-intercept of $f$ becomes the $x$-intercept of $f^{-1}$.
The point $(c,0)$ on $f^{-1}$. The $y$-intercept of $f$ becomes the $x$-intercept of $f^{-1}$.
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Identify the point on $f^{-1}$ that corresponds to the $x$-intercept $(c,0)$ of $f$.
Identify the point on $f^{-1}$ that corresponds to the $x$-intercept $(c,0)$ of $f$.
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The point $(0,c)$ on $f^{-1}$. The $x$-intercept of $f$ becomes the $y$-intercept of $f^{-1}$.
The point $(0,c)$ on $f^{-1}$. The $x$-intercept of $f$ becomes the $y$-intercept of $f^{-1}$.
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What is $f^{-1}(-6)$ if the graph of $f$ includes $(2,-6)$?
What is $f^{-1}(-6)$ if the graph of $f$ includes $(2,-6)$?
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$f^{-1}(-6)=2$. Read the $x$-coordinate where the graph has $y=-6$.
$f^{-1}(-6)=2$. Read the $x$-coordinate where the graph has $y=-6$.
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What is $f^{-1}(1)$ if the graph of $f$ includes $( rac{1}{2},1)$?
What is $f^{-1}(1)$ if the graph of $f$ includes $( rac{1}{2},1)$?
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$f^{-1}(1)= rac{1}{2}$. Read the $x$-coordinate where the graph has $y=1$.
$f^{-1}(1)= rac{1}{2}$. Read the $x$-coordinate where the graph has $y=1$.
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What point lies on $f^{-1}$ if the point $(0,-7)$ lies on $f$?
What point lies on $f^{-1}$ if the point $(0,-7)$ lies on $f$?
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$(-7,0)$ lies on $f^{-1}$. Inverse functions swap the coordinates of points.
$(-7,0)$ lies on $f^{-1}$. Inverse functions swap the coordinates of points.
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What is $f^{-1}(-1)$ if a graph of $f$ shows $f(6)=-1$?
What is $f^{-1}(-1)$ if a graph of $f$ shows $f(6)=-1$?
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$f^{-1}(-1)=6$. Find the input that produces output $-1$.
$f^{-1}(-1)=6$. Find the input that produces output $-1$.
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Identify the domain of $f$ if the range of $f^{-1}$ is $(0,10)$.
Identify the domain of $f$ if the range of $f^{-1}$ is $(0,10)$.
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The domain of $f$ is $(0,10)$. Domain and range swap between inverse functions.
The domain of $f$ is $(0,10)$. Domain and range swap between inverse functions.
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What is $f^{-1}(7)$ if a table shows $f(2)=7$?
What is $f^{-1}(7)$ if a table shows $f(2)=7$?
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$f^{-1}(7)=2$. The inverse reverses the input-output pair $(2,7)$.
$f^{-1}(7)=2$. The inverse reverses the input-output pair $(2,7)$.
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What is $f^{-1}(0)$ if a table shows $f(-4)=0$?
What is $f^{-1}(0)$ if a table shows $f(-4)=0$?
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$f^{-1}(0)=-4$. The inverse reverses the input-output pair $(-4,0)$.
$f^{-1}(0)=-4$. The inverse reverses the input-output pair $(-4,0)$.
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