## Standards derived from the same national standard

Using graphs, tables, or successive approximations, show that the solution to the equation π(π₯) = π(π₯) is the π₯-value where the π¦-values of π(π₯) and π(π₯) are the same.

Explain why the πΉ-coordinates of the points where the graphs of the equations πΊ = π§(πΉ) and πΊ = π(πΉ) intersect are the solutions of the equation π§(πΉ) = π(πΉ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where π§(πΉ) and/or π(πΉ) are polynomial, rational, and logarithmic functions.

Explain why the πΉ-coordinates of the points where the graphs of the equations πΊ = π§(πΉ) and πΊ = π(πΉ) intersect are the solutions of the equation π§(πΉ) = π(πΉ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where π§(πΉ) and/or π(πΉ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Explain why the πΉ-coordinates of the points where the graphs of the equations πΊ = π§(πΉ) and πΊ = π(πΉ) intersect are the solutions of the equation π§(πΉ) = π(πΉ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where π§(πΉ) and/or π(πΉ) are polynomial, rational, and logarithmic functions.

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately.

Explain why the π₯-coordinates of the points where the graphs of the equations y = π(π₯) and y = π(π₯) intersect are the solutions of the equation π(π₯) = π(π₯); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where π(π₯) and/or π(π₯) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the approximate solutions using technology.

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately (e.g., using technology to graph the functions, make tables of values or find successive approximations). Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential and logarithmic functions.

Explain why the πΉ-coordinates of the points where the graphs of the equations πΊ = π§(πΉ) and πΊ = π(πΉ) intersect are the solutions of the equation π§(πΉ) = π(πΉ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where π§(πΉ) and/or π(πΉ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Explain why the πΉ-coordinates of the points where the graphs of the equations πΊ = π§(πΉ) and πΊ = π(πΉ) intersect are the solutions of the equation π§(πΉ) = π(πΉ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where π§(πΉ) and/or π(πΉ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.