Transformations of Functions - AP Precalculus
Card 1 of 30
What transformation does $-f(x)$ represent?
What transformation does $-f(x)$ represent?
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Reflection across the x-axis. Negative sign flips graph over the horizontal axis.
Reflection across the x-axis. Negative sign flips graph over the horizontal axis.
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What is the effect of $f(x - c)$ on the graph of $f(x)$?
What is the effect of $f(x - c)$ on the graph of $f(x)$?
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Horizontal shift right by $c$ units. Subtracting from input moves graph in same direction horizontally.
Horizontal shift right by $c$ units. Subtracting from input moves graph in same direction horizontally.
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What is the effect of $f(x + c)$ on the graph of $f(x)$?
What is the effect of $f(x + c)$ on the graph of $f(x)$?
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Horizontal shift left by $c$ units. Adding to input moves graph opposite direction horizontally.
Horizontal shift left by $c$ units. Adding to input moves graph opposite direction horizontally.
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What is the effect of $f(x) - c$ on the graph of $f(x)$?
What is the effect of $f(x) - c$ on the graph of $f(x)$?
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Vertical shift downward by $c$ units. Subtracting constant from function output moves graph down.
Vertical shift downward by $c$ units. Subtracting constant from function output moves graph down.
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Identify the transformation: $f(x) = |x|$ to $f(x) = 3|x|$
Identify the transformation: $f(x) = |x|$ to $f(x) = 3|x|$
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Vertical stretch by a factor of 3. Factor 3 multiplies all $y$-values by 3.
Vertical stretch by a factor of 3. Factor 3 multiplies all $y$-values by 3.
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Identify the transformation: $f(x) = |x|$ to $f(x) = |x - 1|$
Identify the transformation: $f(x) = |x|$ to $f(x) = |x - 1|$
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Horizontal shift right by 1 unit. Subtracting 1 from input shifts right by 1.
Horizontal shift right by 1 unit. Subtracting 1 from input shifts right by 1.
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What is the effect of $f(x + c)$ on the graph of $f(x)$?
What is the effect of $f(x + c)$ on the graph of $f(x)$?
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Horizontal shift left by $c$ units. Adding to input moves graph opposite direction horizontally.
Horizontal shift left by $c$ units. Adding to input moves graph opposite direction horizontally.
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What is the effect of $f(cx)$ where $0 < c < 1$?
What is the effect of $f(cx)$ where $0 < c < 1$?
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Horizontal stretch by a factor of $\frac{1}{c}$. Input coefficient less than 1 stretches horizontally.
Horizontal stretch by a factor of $\frac{1}{c}$. Input coefficient less than 1 stretches horizontally.
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Identify the transformation: $f(x) = x^3$ to $f(x) = x^3 - 2$
Identify the transformation: $f(x) = x^3$ to $f(x) = x^3 - 2$
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Vertical shift downward by 2 units. Subtracting 2 from output moves graph down.
Vertical shift downward by 2 units. Subtracting 2 from output moves graph down.
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What is the effect of $cf(x)$ where $c > 1$?
What is the effect of $cf(x)$ where $c > 1$?
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Vertical stretch by a factor of $c$. Multiplying by factor greater than 1 stretches vertically.
Vertical stretch by a factor of $c$. Multiplying by factor greater than 1 stretches vertically.
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What transformation does $f(x) = x^2$ to $f(x) = -x^2$ represent?
What transformation does $f(x) = x^2$ to $f(x) = -x^2$ represent?
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Reflection across the x-axis. Negative sign flips parabola across $x$-axis.
Reflection across the x-axis. Negative sign flips parabola across $x$-axis.
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What transformation is applied: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{(x-4)}$?
What transformation is applied: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{(x-4)}$?
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Horizontal shift right by 4 units. Subtracting 4 from input shifts right by 4.
Horizontal shift right by 4 units. Subtracting 4 from input shifts right by 4.
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Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} + 7$
Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} + 7$
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Vertical shift upward by 7 units. Adding 7 to function output shifts upward.
Vertical shift upward by 7 units. Adding 7 to function output shifts upward.
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What is the effect of $f(x)$ to $-f(x)$ on its range?
What is the effect of $f(x)$ to $-f(x)$ on its range?
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Negate each element of the range. Reflection flips signs of all output values.
Negate each element of the range. Reflection flips signs of all output values.
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What is the effect of $f(x)$ to $f(-x)$ on its domain?
What is the effect of $f(x)$ to $f(-x)$ on its domain?
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Negate each element of the domain. Reflection changes signs of all input values.
Negate each element of the domain. Reflection changes signs of all input values.
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Identify the transformation: $f(x) = x^3$ to $f(x) = (x + 4)^3$
Identify the transformation: $f(x) = x^3$ to $f(x) = (x + 4)^3$
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Horizontal shift left by 4 units. Adding 4 to input moves graph left by 4.
Horizontal shift left by 4 units. Adding 4 to input moves graph left by 4.
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What is the effect of $f(x)$ to $f(x + c)$ on its domain?
What is the effect of $f(x)$ to $f(x + c)$ on its domain?
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Subtract $c$ from each element of the domain. Horizontal shift adjusts input values by constant.
Subtract $c$ from each element of the domain. Horizontal shift adjusts input values by constant.
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What transformation does $f(-x)$ represent?
What transformation does $f(-x)$ represent?
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Reflection across the y-axis. Negative input creates mirror image across vertical axis.
Reflection across the y-axis. Negative input creates mirror image across vertical axis.
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What is the effect of $f(x) + c$ on the graph of $f(x)$?
What is the effect of $f(x) + c$ on the graph of $f(x)$?
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Vertical shift upward by $c$ units. Adding constant to function output moves graph up.
Vertical shift upward by $c$ units. Adding constant to function output moves graph up.
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What is the effect of $cf(x)$ where $0 < c < 1$?
What is the effect of $cf(x)$ where $0 < c < 1$?
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Vertical compression by a factor of $c$. Multiplying by factor less than 1 compresses vertically.
Vertical compression by a factor of $c$. Multiplying by factor less than 1 compresses vertically.
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What is the effect of $cf(x)$ where $c > 1$?
What is the effect of $cf(x)$ where $c > 1$?
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Vertical stretch by a factor of $c$. Multiplying by factor greater than 1 stretches vertically.
Vertical stretch by a factor of $c$. Multiplying by factor greater than 1 stretches vertically.
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What transformation is applied: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{(x-4)}$?
What transformation is applied: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{(x-4)}$?
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Horizontal shift right by 4 units. Subtracting 4 from input shifts right by 4.
Horizontal shift right by 4 units. Subtracting 4 from input shifts right by 4.
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What transformation does $f(x) = x^2$ to $f(x) = (x + 5)^2$ represent?
What transformation does $f(x) = x^2$ to $f(x) = (x + 5)^2$ represent?
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Horizontal shift left by 5 units. Adding 5 to input shifts left by 5 units.
Horizontal shift left by 5 units. Adding 5 to input shifts left by 5 units.
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Identify the transformation: $f(x) = |x|$ to $f(x) = |x - 1|$
Identify the transformation: $f(x) = |x|$ to $f(x) = |x - 1|$
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Horizontal shift right by 1 unit. Subtracting 1 from input shifts right by 1.
Horizontal shift right by 1 unit. Subtracting 1 from input shifts right by 1.
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Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} + 7$
Identify the transformation: $f(x) = \frac{1}{x}$ to $f(x) = \frac{1}{x} + 7$
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Vertical shift upward by 7 units. Adding 7 to function output shifts upward.
Vertical shift upward by 7 units. Adding 7 to function output shifts upward.
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Identify the transformation of $f(x) = x^2$ to $f(x) = 2x^2 + 3$.
Identify the transformation of $f(x) = x^2$ to $f(x) = 2x^2 + 3$.
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Vertical stretch by 2 and shift up by 3. Multiplies output by 2, then adds 3 to result.
Vertical stretch by 2 and shift up by 3. Multiplies output by 2, then adds 3 to result.
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What is the effect of $f(cx)$ where $0 < c < 1$?
What is the effect of $f(cx)$ where $0 < c < 1$?
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Horizontal stretch by a factor of $\frac{1}{c}$. Input coefficient less than 1 stretches horizontally.
Horizontal stretch by a factor of $\frac{1}{c}$. Input coefficient less than 1 stretches horizontally.
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What is the effect of $f(x)$ to $f(x) + c$ on its range?
What is the effect of $f(x)$ to $f(x) + c$ on its range?
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Add $c$ to each element of the range. Vertical shift adds constant to all output values.
Add $c$ to each element of the range. Vertical shift adds constant to all output values.
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What is the effect of $f(x)$ to $f(x + c)$ on its domain?
What is the effect of $f(x)$ to $f(x + c)$ on its domain?
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Subtract $c$ from each element of the domain. Horizontal shift adjusts input values by constant.
Subtract $c$ from each element of the domain. Horizontal shift adjusts input values by constant.
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What is the effect of $f(x)$ to $-f(x)$ on its range?
What is the effect of $f(x)$ to $-f(x)$ on its range?
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Negate each element of the range. Reflection flips signs of all output values.
Negate each element of the range. Reflection flips signs of all output values.
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