Pre-Calculus Honors Lesson 1.5: Analyzing Graphs of Functions
F: (1) Find the zeros of f (x): f (x) = 2x2 – 7x – 30
(2) Find the zeros and vertical asymptotes: f (x) =
(3) Find the zeros of f (x) x3 – 4x2 – 9x + 36
(4) Find the zeros of f (x) =
(5) Find the zeros of f (x) =
(6) Solve for x: x4 – 10x2 + 9 = 0
I: How to find maxima and minima with your TI-84:
2nd-CALC
Maxima (or Minima)
Left Bound
Right Bound
Guess
Find any local maxima or minima.
(47) f (x) = 3x2 – 2x – 5
(51) h(x) = x3 – 3x2 – x – 1
(53) f (x) =
How to find intervals where f (x) is increasing or decreasing
(55) f (x) = 4 – x
(57) f (x) = 9 – x2
(59) f (x) =
V: Vocabulary (see next page)
E: Pages 56-59 #1-6(omit), 11-63 odd; Graphing Calculator needed!
S: Check odd answers in your textbook
------
Solutions to Warm-Up Questions
(1) x = 6, x =
(2) zero: x = 0; Vertical asymptotes: x = f (x) =
(3) x = ±3, x = 4
(4) x =
(5) x =
(6) x = ±1, ±3
Pre-Calculus Lesson 1.5 Vocabulary
Vertical Line Test: If any line passes through the graph of an equation more than once, the equation is NOT a function
Zeros, x-intercepts, roots, solutions: the x-value(s) of a function when the y-value equals zero
Increasing: a function is increasing on an interval when the graph goes uphill from left to right
Decreasing: a function is decreasing on an interval when the graph goes downhill from left to right
Maximum: the highest point on a function or a given interval; the plural of maximum is maxima
Minimum: the lowest point on a function or a given interval; the plural of minimum is minima
Average rate of change: slope
Secant line: a line that crosses a curve in two points
Tangent line: a line that touches a curve in exactly one point
Odd function: a function with origin symmetry, 180º rotational symmetry; Algebraically, an odd function occurs when f (–x) = –f (x).
Even function: a function with y-axis symmetry; Algebraically, an even function occurs when
f (–x) = f (x).
------
Reminder: Summer Project Test Retake
Thursday, September 24, 2015 2:00-3:00pm
Friday, September 25, 2015 6:50-7:50am and 3:00-4:00pm
10% penalty for retaking the test; 60% maximum score; You will KEEP THE RETAKE SCORE, not the best score. Tutoring help is available in the library at lunchtime M-F.