Question Type 1: Graphing functions Bootcamps

Sketch the graph of $y = 2x - 4$. Show the $x$- and $y$-intercepts and the gradient.

Sketch the graph of $y = (x-3)^2 - 4$. Show the vertex, axis of symmetry, and intercepts.

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

Sketch the graph of $y = (x+1)(x-2)^2$. Show the intercepts, behavior at each root, and end behavior.

Sketch the graph of $y = \sqrt{x+2} - 1$. Indicate the domain and intercepts.

Sketch the graph of $y = \dfrac{6}{x-2}$. Show the asymptotes and intercepts, and indicate the branches.

Sketch the graph of $y = \dfrac{3x - 6}{x + 2}$. Show the vertical and horizontal asymptotes and the intercepts.

Sketch the graph of $y = |2x - 6| - 4$. Show the vertex and intercepts.

Sketch the graph of $y = \dfrac{x+1}{x-3}$. Show the vertical and horizontal asymptotes and the intercepts.

Sketch the graph of $y = x^3 - 3x$. Show all intercepts, stationary points, and the nature of each stationary point.

Sketch the graph of $y = \dfrac{x^2-1}{x-1}$. Identify any discontinuities and key features.

Sketch the graph of $y = \dfrac{x^2}{x-1}$. Show intercepts, vertical and oblique asymptotes, and indicate which side of the oblique asymptote the curve lies for large $|x|$.