CPM Homework Help : A2C Problem 13-33

Graph $f(x) = 1 +$ tan $(x -\frac { \pi } { 4 })$ .

Hint 1:

Here is the original graph of $f(x) =$ tan $(x)$ .
Repeating increasing curves, with first visible curve, contained within vertical asymptotes, negative pi halves & pi halves, changing from opening down, to opening up, at the origin. Additional visible curves cross the x axis at pi & 2 pi.

Hint 2:

How does adding $1$ shift the graph?

Hint 3:

How does subtracting $\frac{\pi }{4}$ from $x$ shift the graph?

Answer:

Added to graph, repeating increasing red curves, with first visible curve, contained within vertical asymptotes, negative pi fourths & 3 pi fourths, changing from opening down, to opening up, at the point, (pi fourths, comma 1). Additional visible curves cross the x axis at pi, 2 pi, & 3 pi.