- representing in words, ordered pairs, tables of values, graphs, function notation, and equations
- determining characteristics including intercepts, slope, domain, and range
- relating different equation forms to each other and to graphs.
[C, CN, PS, R, T, V]
| (a) |
Critique the statement “any straight line is the graph of a linear function”. |
| (b) |
Explain, using examples, the impact of the domain of a linear function on the graph of the function (e.g., if the domain is not all Real numbers, then the graph will not show a solid line). |
| (c) |
Analyze situations to identify, with justification, the independent and a dependent variable. |
| (d) |
Analyze situations, graphs, tables of values, equations, or sets of ordered pairs to determine if the relationship described is linear. |
| (e) |
Match corresponding types of representations of linear relations (e.g., situations, graphs, tables of values, equations, and sets of ordered pairs). |
| (f) |
Develop, generalize, explain, and apply strategies for determining the intercepts (as values and ordered pairs) of a linear relation from its graph. |
| (g) |
Determine the slope, domain, and range of the graph of a linear relation. |
| (h) |
Sketch examples of linear relations to demonstrate the number of x or y intercepts possible for any line. |
| (i) |
Match, with explanation, slopes and y-intercepts to graphs of linear relations. |
| (j) |
Solve a situational question that involves the intercepts, slope, domain, or range of a linear relation. |
| (k) |
Express the equation of a linear relation in different forms (including the slope-intercept or general form) and compare the graphs of the linear relations. |
| (l) |
Generalize, explain, and apply strategies for drawing or sketching the graph of a linear relation in slope-intercept, general, or slope-point form, or function notation. |
| (m) |
Graph, with and without technology, a linear relation given in slope-intercept, general, or slope-point form, and explain the strategy used to create the graph. |
| (n) |
Analyze a set of linear relations for equivalent linear relations (e.g., $2x + 3y = 6$ is equivalent to $4x + 6y = 12$ ) and explain the reasoning. |
| (o) |
Explain the relationship between linear functions written in function notation and written as equations with two variables, and how to change between the two forms. |
| (p) |
Apply knowledge and skills related to function notation to solve situational questions. |
| (q) |
Determine the related range value, given a domain value for a linear function (e.g., if $f(x) = 3x – 2$, determine $f(–1)$ ) and explain what the resulting value tells about the linear function. |
| (r) |
Determine the related domain value, given a range value for a linear function (e.g., if $g(t) = 7 + t$, determine t so that $g(t) = 15$) and explain what the resulting value tells about the linear function. |
| (s) |
Explain why a linear function would never have a term of $x^2$ when in simplified form. |
