Learning Goals

Section 1 Learning Goals

In this section we give a list of learning goals for this notes. At the beginning of each section starting from Section 2, you will see a list of learning goals that will be addressed in that particular section.

1L: Be able to solve a linear equation.
2L: Be able to determine the slope and the equation of a linear function given its graph or a table of values.
3L: Be able to model a situation with appropriate linear functions and interpret the solution.
4Q: Be able to solve a quadratic equation.
5Q: Be able to determine the vertex and the equation of a quadratic function given its graph or a table of values.
6Q: Be able to model a situation with appropriate quadratic functions and interpret the solution including interpreting the vertex in context.
7E: Be able to solve an equation that has an unknown exponent.
8E: Be able to determine the equation of a function of exponential type given its graph or a table of values.
9E: Be able to model a situation with appropriate functions of exponential type and interpret the solution.
10E: Be able to solve an equation that has logarithmic expressions.
11E: Be able to use the definitions and properties of exponential and logarithmic functions to rewrite or simplify algebraic expressions.
12E: Be able to use the definitions and properties of exponential and logarithmic functions to change their bases.
13F: Be able to determine inputs and outputs of a function from its graph and/or a table of values.
14F: Be able to determine the domain and range of function given as an equation or a graph.
15F: Be able to perform arithmetic (sum, difference, product, quotient) on functions given in any form (graph, table, equation).
16F: Be able to determine a composition of functions given in any form. (graph, table, equation).
17F: Be able to determine the inverse of a function given in any form (graph, table, equation).
18F: Be able to compute the average rate of change of a given function on a given interval.
19F: Be able to produce a graph of a given rational function and indicating the vertical and the horizontal asymptotes.
20F: Be able to solve inequalities and interpret the solution.
21F: Be able to identify the intervals on which a given function is increasing or decreasing.
22F: Be able to determine an appropriate function class (linear, quadratic, exponential, trigonometric) to model a particular situation.
23F: Be able to determine and describe a transformation (translations, compressions, stretches, reflections) of a function given in forms of graphs or equations.
24T: Be able to convert degrees and radians.
25T: Be able to determine the length of an arc of a circle or the area of a sector of a circle.
26T: Be able to use the distance formula or the equation of a circle in context.
27T: Be able to determine an angle or its trigonometric values given other trigonometric values and the quadrant.
28T: Be able to determine the equation of a trigonometric function given its graph.
29T: Be able to simplify functions using triangles that involve trigonometric and anti-trigonometric functions.
30T: Be able to prove trigonometric identities.