I need help with problems from A-J . Thanks in advance! Chapter 2 Test, pages 23
ID: 2911434 • Letter: I
Question
I need help with problems from A-J . Thanks in advance!
Chapter 2 Test, pages 236 Jo DITIONAL PROBLEMS: Are the following statements true or false? Explain your answers. a) If R is a function of S, then S is a function of R b) The average rate of change of a function H with respect to t over an interval can be symbolically represented as c) If fis an increasing function, then the average rate of change of fon any interval is AH positive d) A linear function can have different rates of change over different intervals e) The equation of a line parallel to the x-axis could be x f) The slope of a line parallel to the y-axis is undefined. g) If f (x)-r then f(x + h) =x'+ h) If f (x) +5 and its domain is 12srs21, then its range is 21s ys33 i) If f(x)-x and g(x) (), then for all x, f(x)-glr) j) If f(x)-and g(x), then for all x, f(x)-gx) 4Explanation / Answer
a) False. y=x^2 is a function, however, x=y^2 is not.
b) False. H should come at top and t at bottom. So, deltaH/delta t.
c) True, because for increase in x, y also increases.
d) False. Rate of change or slope is constant.
e) False. It should have been y=-2/5 and not x=-2/5.
f) True. Line paralell to y axis makes 90 degree angle with x axis. Slope = tan theta = tan 90 = undefined.
g) False. f(x+h) = (x+h)^2 = (x+h)(x+h) = x^2 + h^2 + 2xh
i) True. Square of a number is always positive.
j) False. x^2 and (-x)^2 are same. However, x^2 and -x^2 are not same.