High School · Building Functions

CCSS.MATH.CONTENT.HSF.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Read this standard on the official Common Core site

Lessons that teach this standard

• Transformations of Functions: Shifts, Stretches and Reflections

  What each change to f(x) does to its graph, why a change inside the parentheses moves the graph the opposite way, and how to read the constants off a picture.

• Even and Odd Functions: Symmetry of Graphs

  Test whether a function is even, odd or neither by computing f(−x), and see the answer in its graph: a mirror image in the y-axis or a half turn about the origin.

• Graphs of Exponential and Logarithmic Functions

  Graph y = bˣ and y = log_b x: growth and decay, asymptotes, domain and range, the mirror image in y = x, and shifts and stretches of both.