MATA30H3 Lecture Notes - Asymptote

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ceruleanllama424

7 May 2013

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An exponential function of the form y = bx , b > 0, b not equal 1, Has a domain x e r a range y e r, y > 0 a y-intercept of 1. Has a horizontal asymptote at y = 0 is increasing on its domain when b > 1 is decreasing on its domain when 0 < b < 1. The inverse of y = bx is a function that can be written as x = by. Has a domain of x e r, x > 0 a range of y e r a x-intercept of 1. Logarithms a logarithmic function is the inverse of the exponential function. The value of logbx is equal to the exponent to which the base, b, is raised to produce product x. Exponnetial equations can be written in logarithmic form, and vice versa. Y = b^x x = logby. Y = logbx x = b^y.

Related Questions

3. (a) Assume that a function f(x) is concave down on its whole domain, and f(0) = -2 and f'(0) = -1. Circle each statement that must be true: • The function f(2) has no inflection points. • The derivative f'(2) is always negative. • The derivative satisfies f'(3) < -1. • The derivative satisfies f'(-3) < -1. • The function f(x) <-2 for all 1 >0. (b) Sketch a graph of a function f() satisfying all of the following conditions: • The derivative function f'(x) is decreasing when x < 1 and when r > 3. • The derivative function f'(2) is increasing when 1

Sketch the graph of a continious function y=f(x) that satisies thefollowing conditions: a) f(x) is increasing for all x>2,decreasing for x<2 b) f''(x) >0 if x<3 and f''(x) <0 ifx>3

For each graph below, identify the intercepts, domain, range, continuity, and behavior, extrema, and average rate of change.

(a) x-intercept: ____________ (a) x-intercept: _____________

(b) y-intercept: ____________ (b) y-intercept: _____________

(d) Range: ________________ (d) Range: _________________

(e) x ________________ (e) x _________________

(f) x - _____________ (f) x - _________________

(g) Local maxima __________ (g) Local maxima _____________

(h) Global maxima _________ (h) Global maxima ____________

(i) Local maxima __________ (i) Local maxima ______________

(j) Global maxima _________ (j) Global maxima _____________

(k) Avg. ROC - 1.5 < x < 1.5 ____ (k) Avg. ROC - 1.5 < x < 1.5 ____

7. Do you think that average rate of change is always an accurate measure of how a graph changes? Why or why not?