What is a horizontal compression by a factor of 1 3?
What is a horizontal compression by a factor of 1 3?
We can see that the input values decreased by 1/3, so the scale factor applied on f(x) is 3, and so, g(x) = f(3x). This means that the function g(x) is the result of f(x) being horizontally compressed by a scale factor of 3.
What is a horizontal stretch by a factor of 3?
If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.
How do you find the horizontal stretch factor?
If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Given a function y=f(x) y = f ( x ) , the form y=f(bx) y = f ( b x ) results in a horizontal stretch or compression. Consider the function y=x2 y = x 2 .
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 – ). Example: f (x) = 2×2.
What does it mean to shrink a graph horizontally?
A horizontal stretch or shrink by a factor of 1/k means that the point (x, y) on the graph of f(x) is transformed to the point (x/k, y) on the graph of g(x).
How do you stretch horizontally?
Key Points
- 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 ) .
Is vertical stretch and horizontal compression the same?
With a parabola whose vertex is at the origin, a horizontal stretch and a vertical compression look the same.
What is the horizontal stretch factor?
What does horizontally stretched mean?
A horizontal stretching is the stretching of the graph away from the y-axis. A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis. • if k > 1, the graph of y = f (k•x) is the graph of f (x) horizontally shrunk (or compressed) by dividing each of its x-coordinates by k.
How do you compress a graph horizontally?
To shrink or compress horizontally by a factor of c, replace y = f(x) with y = f(cx). Note that if |c|<1, that’s the same as scaling, or stretching, by a factor of 1/c.
What’s the difference between horizontal and vertical?
A vertical line is any line parallel to the vertical direction. A horizontal line is any line normal to a vertical line. Vertical lines do not cross each other.
What are the scale factors of a horizontal stretch?
We can see two scale factors applied to n (x): 3 on the output value and 1/4 for the input value. Applying what we know on vertical and horizontal stretches, we have n (x) = 3·m (1/4 · x). Meaning, n (x) is the result of m (x) being vertically stretched by a scale factor of 3 and horizontally stretched by a scale factor of 1/4.
How are horizontal stretches and compressions related in Algebra?
A General Note: Horizontal Stretches and Compressions 1 If b > 1 b > 1, then the graph will be compressed by 1 b 1 b. 2 If 0 < b< 1 0 < b < 1, then the graph will be stretched by 1 b 1 b. 3 If b < 0 b < 0, then there will be combination of a horizontal stretch or compression with a horizontal reflection.
Which is an example of a horizontal stretch?
A horizontal stretch can be applied to a function by multiplying its input values by a scale factor, a, where 0 < 1/a < 1. What does this mean for functions such as f (x)? When 1/a is multiplied to x, f (x)’s graph stretches horizontally by a scale factor of a.
What happens when a function is horizontally stretched by a factor?
When a function is horizontally stretched by a factor, k, the x-value of the function is multiplied by the factor k. Thus, given the parent function , a horizontal stretch by a factor of means that the x-value of the function is multiplied by . Thus, after a horizontal stretch by a factor of of the parent function , we have .