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**

- 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 ) .

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.