options: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
problem_activity: Task
Sketch the graphs of the functions described by $\displaystyle f(x)=x^2$ and $\displaystyle g(x)=x^4$ on the same axes, being careful to label any points of intersection.  Also, find and label $\displaystyle\left(\frac{1}{2}, f(\frac{1}{2})\right)$ and $\displaystyle\left(\frac{1}{2}, g(\frac{1}{2})\right)$.
Sketch the graphs of the functions described by $f(x)=x^3$ and $g(x)=x^5$ on the same axes, being careful to label any points of intersection. Also, find and label $\displaystyle\left(\frac{1}{2}, f(\frac{1}{2})\right)$ and $\displaystyle\left(\frac{1}{2}, g(\frac{1}{2})\right)$.
Sketch the graphs of the functions described by $f(x)=x^2$ and $g(x)=x^3$ on the same axes, being careful to label any points of intersection. Also, find and label $\displaystyle\left(\frac{1}{2}, f(\frac{1}{2})\right)$ and $\displaystyle\left(\frac{1}{2}, g(\frac{1}{2})\right)$.


correct_option_index: 0