Transformations of functions

Algebra 2 - Shifting Functions Up, Down, Left, and Right

Learn how function transformations shift graphs vertically and horizontally. Understand why adding outside moves up/down while subtracting inside moves right/left.

Algebra 2 - Writing Shifted Functions from Graphs

Learn how to write shifted functions by comparing key points on graphs. Covers horizontal and vertical transformations using the pattern g(x) = f(x - h) + k.

Algebra 2 - Reflecting Functions Over the Axes

Learn how function reflections work: negative f(x) flips graphs over the x-axis, while f(negative x) flips over the y-axis. Visual examples show how signs change.

Algebra 2 - Even and Odd Functions

Learn about even and odd functions, their symmetry properties, and how to identify them graphically using examples like x squared and x cubed.

Algebra 2 - Testing Even and Odd from Equations

Learn the algebraic test for even and odd functions by plugging in negative x and comparing results. Includes examples with polynomial functions.

Algebra 2 - Vertical Scaling: Stretching and Compressing Functions

Learn how vertical scaling transforms functions by multiplying outputs by a constant k, stretching or compressing graphs relative to the x-axis.

Algebra 2 - Horizontal Scaling: Stretching and Compressing Sideways

Learn how horizontal scaling transforms functions using f(kx). Discover why k>1 compresses graphs and 0<k<1 stretches them, with the scale factor being 1/k.

Algebra 2 - Transforming Logarithmic Function Graphs

Learn how to graph transformed logarithmic functions by tracking key points and asymptotes through horizontal shifts, vertical stretches, reflections, and translations.