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Week 8: Algebra - Graphing

Intersecting Graphs (Printable PDF)

Examine the graphs of a line, a parabola, and an exponential function. When any two of these graphs are graphed on the same set of axes, which pair(s) will produce the most intersections? the least intersections? Explain your reasoning.


GPS As seen in Problem Exploration

M8A3: Students will understand relations and linear functions.

i. Identify relations and functions as linear or nonlinear.

j. Translate among verbal, tabular, graphic, and algebraic representations of functions.

The student should be able to translate between the algebraic representation of the functions (equation) and their graphs. The student must also be able to understand how each equation influences its graph.  The student will need to recognize the characteristics of a linear function as compared to a non-linear function.

M8A4: Students will graph and analyze graphs of linear equations.

c. Graph equations of the form y = mx + b.


The student will graph a line in the form of y= mx + b, a parabola in the form of y=ax2+bx+c, and an exponential function, y=kx.

In exploring this investigation, the student should recognize the characteristics of a linear function and be able to identify a linear function versus a non-linear function.