How do you find the transformation of a linear function?

Graphing a Linear Function Using Transformations. Another option for graphing linear functions is to use transformations of the identity function f(x)=x f ( x ) = x . A function may be transformed by a shift up, down, left, or right. A function may also be transformed using a reflection, stretch, or compression.

How does the slope of a linear function act as a transformation?

The graphs of linear functions can be transformed without changing the shape of the line by changing the location of the y intercept or the slope of the line. Those lines can be transformed by translation, rotation, or reflection, and still follow the slope-intercept form y = mx + b.

How do you find the transformation of a function on a point?

Suppose f is a function and h is a positive number. To graph y = f(x + h), shift the graph of y = f(x) left h units by subtracting h from the x-coordinates of the points on the graph of f. To graph y = f(x – h), shift the graph of y = f(x) right h units by adding h to the x-coordinates of the points on the graph of f.

How is the slope of a linear function represented?

The slope of a linear function. The slope of a line is usually represented by the letter m. (x 1, y 1) represents the first point whereas (x 2, y 2) represents the second point. It is important to keep the x-and y-coordinates in the same order in both the numerator and the denominator otherwise you will get the wrong slope.

How to think about the point slope form?

1 One way to think about point-slope form is as a rearrangement of the slope formula. 2 Another way to think about point-slope form is as a transformation of the canonical line y = mx: That is to say, (y – k) = m (x – 3 Also food for thought: Given a point (h,k) and a slope m, the equation

Which is an example of a linear transformation?

Below is the function y = x y = x, compressed by a factor of 1 2 1 2. Now show the vertical shift. The function y = 1 2 x y = 1 2 x shifted down 3 3 units is shown below. The following video example describes another linear transformation of the identity and its corresponding graph.

How to transform a linear function into a graph?

How To: Given the equation of a linear function, use transformations to graph A linear function OF 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 of | m|. Shift the graph up or down b units.