Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)^{n} as the product of P and a factor not depending on P.

Factor a quadratic expression to reveal the zeros of the function it defines.

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^{t} can be rewritten as (1.15^{1/12})^{ 12t }≈ 1.012^{12t} to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Solve equations and inequalities in one variable. [Linear inequalities; literal equations that are linear in the variables being solved for; quadratics with real solutions]

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^{2} = q that has the same solutions. Derive the quadratic formula from this form.

Solve quadratic equations by inspection (e.g., for x^{2} = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Solve systems of equations. [Linear-linear and linear-quadratic]

Understand the concept of a function and use function notation. [Learn as general principle; focus on linear and exponential and on arithmetic and geometric sequences.]

Estimate the rate of change from a graph. Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]

Graph linear and quadratic functions and show intercepts, maxima, and minima.

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^{t} , y = (0.97)^{t} , y = (1.01)^{12t}, and y = (1.2)^{t/10}, and classify them as representing exponential growth or decay.

Determine an explicit expression, a recursive process, or steps for calculation from a context.

Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

Informally assess the fit of a function by plotting and analyzing residuals.

Fit a linear function for a scatter plot that suggests a linear association.

Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)^{n} as the product of P and a factor not depending on P.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

Build new functions from existing functions. [Include simple radical, rational, and exponential functions; emphasize common effect of each transformation across function types.]

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x3 or f(x) = ^{(x + 1)}/_{(x − 1) }for x ≠ 1.