Stitz-Zeager_College_Algebra_e-book

# If x y is on the graph of f then y f x so replacing

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ng x + 2 = a gives x = a − 2 so that g (a − 2) = f ((a − 2) + 2) = f (a) = b. As such, (a − 2, b) is on the graph of y = g (x). The point (a − 2, b) is exactly 2 units to the left of the point (a, b) so the graph of y = g (x) is obtained by shifting the graph y = f (x) to the left 2 units, as pictured below. y y (5, 5) (3, 5) 5 5 4 4 (2, 3) (0, 3) 3 (4, 3) (2, 3) 2 2 (−2, 1) (0, 1) −2 −1 1 2 3 4 5 x shift left 2 units 1 −2 −1 1 2 3 4 5 x −− − − − −→ −−−−−− y = f (x) subtract 2 from each x-coordinate y = g (x) = f (x + 2) Note that while the ranges of f and g are the same, the domain of g is [−2, 3] whereas the domain of f is [0, 5]. In general, when we shift the graph horizontally, the range will remain the same, but the domain could change. If we set out to graph j (x) = f (x − 2), we would ﬁnd ourselves adding 1.8 Transformations 87 2 to all of the x values of the points on the graph of y = f (x) to eﬀect a shift to the right 2 units. Generalizing, we have the following result. Theo...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern