How do you shift reflect and stretch on a graph?

First reflect the graph in the x-axis. Then shift the graph three units to the left. If c > 1 then the graph of y = cf(x) is the graph of y = f(x) stretched vertically by c. If 0 < c < 1 then the graph of y = cf(x) is the graph of y = f(x) shrunk vertically by c.

One simple kind of transformation involves shifting the entire graph of a function up, down, right, or left. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function.

One may also ask, how do you find the stretch factor of a graph? Key Points

  1. When by either f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.
  2. In general, a vertical stretch is given by the equation y=bf(x) y = b f ( x ) .
  3. In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ) .

In this regard, how do you stretch and shrink a graph?

Stretches and Shrinks. We can also stretch and shrink the graph of a function. 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 ).

What does F 2x mean?

f stands for function, so there will be an expression or a formula associated with it: like x^2 or 2x+1, could be anything, but in general: f(2x) means it takes 2x to get the same y, so the curve will be squished horizontally (x is only worth half its previous value, so it has to work twice as hard); and 2f(x) is the

What are the 4 types of transformations?

There are four main types of transformations: translation, rotation, reflection and dilation.

How do you move a graph horizontally?

Horizontally translating a graph is equivalent to shifting the base graph left or right in the direction of the x-axis. A graph is translated k units horizontally by moving each point on the graph k units horizontally. g(x) = f (x – k), can be sketched by shifting f (x) k units horizontally.

How do you shift a function?

– The equation y = f(x + c) shifts the graph of y = f(x) to the left c units. (Adding a constant inside the function shifts the graph left.) – The equation y = f(x − c) shifts the graph of y = f(x) to the right c units. (Subtracting a constant inside the function shifts the graph right.)

How do you scale a function?

Shifting and scaling a function We can add some constants to the functions that will allow us to shift and scale it: . First, let us shift the function along the y-axis. Next, let us shift the function along the x-axis. First, let us scale along the y-axis. Next, let us scale along the x-axis.

What is a even function?

Even Function. A function with a graph that is symmetric with respect to the y-axis. A function is even if and only if f(–x) = f(x).

How do you compress a graph?

How To: Given a function, graph its vertical stretch. 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

How do you shift a parabola?

If you want to move the parabola to the right, say, 4 units, then you must subtract 4 from x and then square that result to get your y-coordinate. So, if you wish to move the reference parabola to the right, subtract a positive number from x.

What is a Parangula?

What is a parangula? you ask! Well, my friends, a parangula—like a line or a parabola—is a geometric object described algebraically, which you may transform by translating, stretching, squishing, and reflecting in order to learn some general algebraic tools for working with these in the future.

How do you find the inverse of a function?

Given the function f(x) we want to find the inverse function, f−1(x) f − 1 ( x ) . First, replace f(x) with y . Replace every x with a y and replace every y with an x . Solve the equation from Step 2 for y . Replace y with f−1(x) f − 1 ( x ) .

How do you tell if a graph shrinks or stretches?

if 0 < k < 1 (a fraction), the graph is f (x) vertically shrunk (or compressed) by multiplying each of its y-coordinates by k. if k should be negative, the vertical stretch or shrink is followed by a reflection across the x-axis. Notice that the "roots" on the graph stay in their same positions on the x-axis.

How do you know if a graph is stretched or compressed?

If a > 1 displaystyle a>1 a>1, then the graph will be stretched. If 0 < a < 1, then the graph will be compressed. If a < 0 displaystyle a<0 a<0, then there will be combination of a vertical stretch or compression with a vertical reflection.