Question Type 1: Graphing functions Exercises

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

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

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

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

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

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

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 $y = (x-1)(x+2)(x-3)$, labeling all intercepts and end behavior; indicate the approximate locations of turning points.

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

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