F x x 3 horizontal stretch
[PDF File]Graphs Shifting, Reflecting, and Stretching
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Let c be a positive real number. Vertical and Horizontal shifts in the graph of y = f(x) and represented as follows. 1. Vertical shifts c units upward: h(x) = f(x) + c 2. Vertical shifts c units downward: h(x) = f(x) - c 3. Horizontal shifts c units to the right: h(x) = f(x-c) 4. Horizontal shifts c units to the left: h(x) = f(x+c) 18
[PDF File]1.2 Transformations of Linear and Absolute Value Functions
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Let f(x) = ∣ x − 3 ∣ − 5. Write (a) a function g whose graph is a horizontal shrink of the graph of f by a factor of 1— 3, and (b) a function h whose graph is a vertical stretch of the graph of f by a factor of 2. SOLUTION a. A horizontal shrink by a factor of —1 3 multiplies each input value by 3. g(x) = f(3x) Multiply the input by 3.
[PDF File]Horizontal Compression/Stretch of y=tan(x)
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3. Period = 2 5. Vertical Asymptotes: x=1+2n, where n is any integer 7. Vertical Asymptotes: x= 1 3 + 2 3 n, where n is any integer 9. Zeros: x= 1 4 n where n is any integer 11. As b increases, the period decreases and the graph is compressed horizontally. As b decreases, the period increases and the graph is stretched horizontally.
[PDF File]Graphing Standard Function & Transformations
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g(x) = x2 + 2 = f(x) + 2 h(x) = x2 – 3 = f(x) – 3 Look for the positive and negative sign. Positive sign makes the graph move upwards and the negative sign makes it move downwards Here is a picture of the graph of g(x) = x2 1. It is obtained from the graph of f(x) = x2 by shifting it down 1 unit.
[PDF File]Graphing I: Transformations and Parent Functions
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If f (x) is the parent ftnction, af(b(x - c)) + d is the transformed ftnction where a is the b is the c is the d is the (-1_9) (-3:9) "stretch" ' compression" "horizontal shift" "vertical shift" Compressed g(x) f(x) (1:9) (3:9) 144 144 Compare: transformation: f (bx) ("compression") h (x) = 4(x) transformation: aý(x) ("stretch")
[PDF File]You should know the graph of the following basic functions
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a horizontal stretch, the y intercept is unchanged. Example: Starting with f 1(x) = x3, we can obtain f 2(x) = f 1 1 2 x = 1 2 x 3. The graph of 1 2 x 3 is the graph of x3 stretched by a factor of 2 horizontally. 1 2 x 3 x3 Again, pay attention to the fact that, in a horizontal stretch/compression that,
[PDF File]Mathematics 11 Page 1 of 3 Horizontal Transformations ...
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y = g 1 x horizontal stretch by 4 1 or horizontal compression by 4 e) y = g(x− 2) −1 shift right by 2 and shift down by 1 f) y = 3g(x+ 1) vertically stretch by 3 and translate up by 1 g) y = 2− g(x) reflect in the x-axis then translate up by 2
[PDF File]1-31-3 Transforming Linear Functions
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Let g(x) be a horizontal shift of f(x) = 3x left 6 units followed by a horizontal stretch by a factor of 4. Write the rule for g(x). Step 1 First perform the translation. Translating f(x) = 3x left 6 units adds 6 to each input value. You can use h(x) to represent the translated function. Add 6 to the input value. Evaluate f at x + 6. Distribute.
[PDF File]2.6 Transformations of Polynomial Functions
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transformations of the graph of f. 10. 32fx x x()=− +32; horizontal stretch by a factor of 3 and a translation 3 units up, followed by a reflection in the x-axis 11. 53 2fx x x x()=−+ +351; reflection in the y-axis and a vertical shrink by a factor of 1 2, followed by a translation 1 unit up 12.
[PDF File]Graphing Radical Functions - Weebly
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Describe the transformation of f (x) = √3 ... In Example 1, notice that the graph of f is a horizontal stretch of the graph of the parent square root function. The graph of g is a vertical stretch and a refl ection in the x-axis of the graph of the parent cube root function. You can transform graphs of
[PDF File]Vertical and Horizontal Shifts of Graphs
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f x x x x o og x h 3 x Note: In part (a), hx can also be written as h x x 3 18. (b) 1 3 63 Right 6 Shrink horizontally by a factor o 6 f f x x g o o xxx h x (c) No, parts (a) and (b) do not yield the same function, since 3 18 3 6xx z . Both graphs are shown below to emphasize the difference in the final results (but we
[PDF File]Communicate Your Answer
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Let f(x) = ∣ x − 3 ∣ − 5. Write (a) a function g whose graph is a horizontal shrink of the graph of f by a factor of 1— 3, and (b) a function h whose graph is a vertical stretch of the graph of f by a factor of 2. SOLUTION a. A horizontal shrink by a factor of —1 3 multiplies each input value by 3. g(x) = f(3x) Multiply the input by 3.
[PDF File]Graphing Functions using Transformations
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Horizontal stretch by a factor of 2 and reflection in the y-axis means that b = − Translation 3 units up means that k = 3 Translation 2 units right means that h = 2 Plugging these values into the general form f(x) = a f[ b(x − h)] + k where f(x) = , we get f(x) = 4[] + 3. This can be simplified to f(x) = + 3.
[PDF File]3.6 Transformations of Graphs of Linear Functions
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148 Chapter 3 Graphing Linear Functions Stretches and Shrinks You can transform a function by multiplying all the x-coordinates (inputs) by the same factor a.When a > 1, the transformation is a horizontal shrink because the graph shrinks toward the y-axis.When 0 < a < 1, the transformation is a horizontal stretch because the graph stretches away from the y-axis.
[PDF File]Transformations of Quadratic Functions - jensenmath
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The graph of g(x) = f(kx) is a horizontal stretch or compression of the graph of f(x) by a factor of Note: a vertical stretch or compression means that distance from the y-axis of each point of the parent function changes by a factor of 1/k. Note: for a horizontal reflection, the point (x, y) becomes
[PDF File]Alg2 1.3 Notes.notebook - Bainbridge Island School District
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Alg2 1.3 Notes.notebook September 05, 2012 f(x) = x + 3 Is this a vertical shift or a horizontal shift? Let g(x) be the indicated transformation of f(x). Write the rule for g(x). Translating f(x) 3 units right subtracts 3 from each input value. I. Translating Linear Functions
[PDF File]3.1 Transformations of Quadratics.notebook
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horizontal stretch (away from y-axis) when 0 < a < I horizontal shrink (toward y-axis) when a > I Reflections in the y-Axis f(x) = x2 ( —x)2 = y = x2 is its own reflection in the y-axis. Vertical Stretches and Shrinks f(x) = _r2 a .f(x) = ax-2 Y = ax2, Y = ax2, vertical stretch (away from x-axis) when a > I vertical shrink (toward x-axis)
[PDF File]4.4 Notes and Examples
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Horizontal Shift Stretch/Compress x-Axis Reflection y-Axis Reflection Vertical Shift O O O O O Left Stretch Yes Yes Up O O O O O Right O None Compress O None No No Doum O None Lesson 4.4 - Transformations of Functions Pre-certify Practice : Question 8 of 20, Step 1 of 2 FUNCTION Consider the following ftnction. SOLUTION
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