Stretch and Compression The stretching or compressing of the absolute value function y=| x | is defined by the function y=a| x | where a is a constant. The graph opens up if a>0 and opens down when a<0.
How do you dilate an absolute value graph?
In absolute value graphs, a dilation makes the V either wider or thinner. We accomplish this by putting a value in front of the absolute value (for example, y=2|x| or y=1/3|x|). Just like the m in y=mx+b, this value tells us the new slope of the lines in our V.
How do you stretch a linear function?
- Graph f(x)=x f ( x ) = x .
- Vertically stretch or compress the graph by a factor of |m|.
- Shift the graph up or down b units.
How do you make a graph skinnier?
A stretch or compression is a function transformation that makes a graph narrower or wider. Stretching a graph means to make the graph narrower or wider.How do you know if a graph is a vertical stretch or compression?
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.
How do you stretch a horizontal function?
- When by either f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.
- In general, a vertical stretch is given by the equation y=bf(x) y = b f ( x ) . …
- In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ) .
How do you reflect absolute value over the y axis?
In reflection about the y -axis, a point (a,b) on the graph of y=f(x) y = f ( x ) moves to a point (−a,b) on the graph of y=f(−x) y = f ( − x ) .
How do you stretch or shrink a graph?
To stretch or shrink the graph in the y direction, multiply or divide the output by a constant. 2f (x) is stretched in the y direction by a factor of 2, and f (x) is shrunk in the y direction by a factor of 2 (or stretched by a factor of ). Here are the graphs of y = f (x), y = 2f (x), and y = x.What is absolute value graph?
Absolute value graphs are linear representations of absolute value functions. These equations are always expressed within absolute value bars. Here is an example: Taking the absolute value of a number or equation cancels out its negative signs.
How do you compress a graph?- Identify the value of a .
- Multiply all range values by a .
- If a>1 , the graph is stretched by a factor of a . If 0<a<1 0 < a < 1 , the graph is compressed by a factor of a . If a<0 , the graph is either stretched or compressed and also reflected about the x -axis.
What makes a function flatter?
Stretches and compressions change the slope of a linear function. If the line becomes steeper, the function has been stretched vertically or compressed horizontally. If the line becomes flatter, the function has been stretched horizontally or compressed vertically. f(x)→f(1bx) • b > 1 stretches away from the y-axis.
How do you vertically stretch a linear graph?
How To: Given the equation of a linear function, use transformations to graph the linear function in the form f(x)=mx+b f ( x ) = m x + b . Graph f(x)=x f ( x ) = x . Vertically stretch or compress the graph by a factor |m|. Shift the graph up or down b units.
What is vertical and horizontal stretch?
vertical stretching/shrinking changes the y -values of points; transformations that affect the y -values are intuitive. horizontal stretching/shrinking changes the x -values of points; transformations that affect the x -values are counter-intuitive.
What is the difference between vertical compression and horizontal stretch?
A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically stretched by multiplying each of its y-coordinates by k. A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis.
What transformation is absolute value?
by performing transformations on the parent function f (x) = |x|. The function f(x) = |x| is an absolute value function. The highest or lowest point on the graph of an absolute value function is called the vertex.
How do you find the stretch factor?
- Refer to: y=af(b(x−h))+k.
- A vertical stretch is the stretching of a function on the x-axis. …
- A horizontal stretch is the stretching of a function on the y-axis. …
- For example: …
- b=12.
- To vertically stretch we use this formula: …
- To horizontally stretch we use this formula: …
- x1=x12.
How do you write a horizontal stretch by a factor of 2?
Thus, the equation of a function stretched vertically by a factor of 2 and then shifted 3 units up is y = 2f (x) + 3, and the equation of a function stretched horizontally by a factor of 2 and then shifted 3 units right is y = f ( (x – 3)) = f ( x – ).
What is the absolute value in math?
Definitions: The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.
