Math 109: Exam 1 review
Directions:
- Find a problem from the book (homework or chapter reviews) that is an example of the objective listed below.
- Work through each of these problems, starting with problems that appear "most
difficult".
- Flag problems/objectives that are still unclear for class discussion.
Algebra (review)
- solve an equation for one variable (evaluate for given input or solve for given output)
- apply operations to equations (+ - × ÷)
- manipulate rational expressions (fractions!)
- manipulate inequalities
Functions
- state and use the definition
- represent functions with: tables, graphs, sets of ordered pairs, function notation
- use the vertical line test
- create a function given a real world situation or one of the above representations
- identify the input (independent variable) and output (dependent variable)
- interpret in a real-world context
Average rate of change
- state and use the definition
- compute the rate of change of a function (given any representation)
- state and use the relationship between a.r.o.c. and linear functions
- state and use the relationship between a.r.o.c. and concavity
- interpret in a real-world context
Linear functions
- state and use the definition
- compute slope
- find intercepts
- create an equation of a line given two points or given slope and a point
- create and use an equation of a line in standard form, point-slope form, or slope-intercept form
- state and use the definition of parallel lines
- state and use the definition of perpendicular lines
- identify and create an equation for a vertical line or horizontal line
- find the intersection point of two lines
- interpret in a real-world context
Domain and Range
- find the domain and range of a function graphically
- find the domain and range of a function algebraically
Piecewise functions
- graph a piecewise function
- create a piecewise function from a graph
Composite functions
- state a composite function given the inside and outside functions
- use both notations for composition, e.g., f(g(x)) or (f o g)(x)
Inverse
- find the inverse of a function
- justify that the inverse is correct
Concavity
- state and use the definition
- identify when a function is concave up/down using tables, graphs, or functions
- identify when a function is increasing/decreasing using tables, graphs, or functions
Quadratic functions
- identify a quadratic function
- find zeros using factoring
- find zeros using the quadratic formula
- use the discriminent to determine if the function will have 0, 1, or 2 real zeros
- interpret in a real-world context