IB Mathematics Applications & Interpretation Question Type 1: Graphing Functions Exercises

Sketch the graph of $y=x^2+4x+5$, labeling the vertex, axis of symmetry, and intercepts; indicate whether there are any $x$-intercepts.

Sketch the graph of $y=-x^2+4x+5$, labeling the vertex, axis of symmetry, and intercepts.

Sketch the graph of $y=-(x-2{)}^2(x+1)$, labeling the intercepts and describing the behavior at the double root.

Sketch the graph of $y=x+\frac{1}{x}$, indicating the vertical asymptote, any intercepts, symmetry, and turning points.

Sketch the graph of $y=\frac{2x+1}{x-3}$, labelling the vertical and horizontal asymptotes and the intercepts.

Sketch the graph of $y=(x-2{)}^2-5$, labeling the vertex, axis of symmetry, and intercepts.

Sketch the graph of $y=-2x+3$, labelling the $x$- and $y$-intercepts.

Calculate the coordinates of the turning points and sketch the graph of $y=(x-1)(x+2)(x-3)$, labeling the intercepts and turning points.

Sketch the graph of $y=\frac{2}{x-1}+3$, labeling the vertical and horizontal asymptotes and the intercepts.

Sketch the graph of $y=\frac{x^2-4x+1}{x-1}$, labeling intercepts and the vertical and oblique (slant) asymptotes.

Sketch the graph of $y=\frac{x^2-1}{x-1}$, indicating any discontinuities (asymptotes or holes) and labeling the intercepts.

Sketch the graph of $y=\frac{6}{x}$, labeling the vertical and horizontal asymptotes and indicating any intercepts.