Common Core · High school
HSF-LE.A.2
High school — Construct an exponential function given a graph, a description of a relationship, or a table of values.
High school — Construct linear functions given a graph, a description of a relationship, or two input-output pairs.
High school — Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input–output pairs.
The 4 skills that cover it
- Exponential FunctionsModel repeated growth and decay with y = a * b^x, and contrast constant differences with constant ratios.Read the lesson →
- Forms of a LineWrite the equation of a line in point-slope, slope-intercept and standard form, convert between the three, read intercepts off standard form, and build parallel and perpendicular lines through a point.Read the lesson →
- Compound Interest & Exponential ModelsTurn a percent rate into a growth factor, compound it monthly, daily or continuously with e, and build the exponential model behind interest, population and half-life problems.Read the lesson →
- Arithmetic & Geometric SequencesSee a list of numbers as a function of its position: tell an arithmetic sequence from a geometric one, write explicit and recursive formulas, and find any term without listing the ones before it.Read the lesson →
What a student should be able to do
- Evaluate an exponential function at a given input.
- Identify growth and decay from the base.
- Write an exponential model from a starting amount and a rate.
- Compare linear and exponential growth over time.
- Write the equation of a line from a point and a slope in point-slope form, and from two points.
- Convert between slope-intercept form y = mx + b and standard form Ax + By = C.
- Find both intercepts of a line given in standard form.
- Write the equation of the line through a point that is parallel or perpendicular to a given line.
- Write an exponential model from a starting amount and a percent growth or decay rate.
- Compute compound interest with n compounding periods per year, and continuous growth with e.
- Model half-life and population change, and find a growth factor from two readings.
- Compare models and rates, including the effective annual rate.
- Identify a sequence as arithmetic or geometric and find its common difference or ratio.
- Write an explicit formula for the nth term and use it to find a given term.
- Write and use a recursive formula, and convert between recursive and explicit forms.
- Find a formula from two given terms.