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Suppose that the functions at and w are defined as follows. u(x)=x+2 w (x): 2x2+1 Find the following. Suppose that the function g is defined, for all real numbers, as follows. 1 ExZ x2 g(x)= 2 x=2 Find g(4), g(2), and g(2). O The function g is defined as g (x)= -5x + 3x Find g (x + 1). Write your answer without parentheses, and simplify it as much as possible. g (x + 1) = [ X 5The entire graph of the function g is shown in the figure below. Write the domain and range of g as intervals or unions of intervals. 5 - 4- 3- domain = (0,0) [0,0] (0,0] 2- range = [0,0) O OVO 2 2 3 - OO -2- -3 X 5 -5 -v Determine the interval()_ on which the function is (strictly) decreasing. Write your answer as an interval or list of intervals. When writing a list of intervals, make sure to separate each interval with a comma and to use as few intervals as possible. Click on "None" if applicable. E El [DD] 00 None ELEL... (EH31 (ELIE) [will -00 For each g@p_h, choose the function that best describes it. (a) - (b) (Choose one) V (Choose one) V (C) - (d) |Z| (Choose one) V (Choose one) V V Suppose that the functionsfand g are defined for all real numbers x as follows. f(x)=3x2 g(x)=x+2 Write the expressions for (gf) (x) and (gf) (x) and evaluate (g+f) ( 1). The graphs of the functions g and h are shown below. For each graph, find the absolute maximum and absolute minimum. If no such value exists, click on "None". Assume that the dashed line shown is a vertical asymptote that the graph does not cross. None (a) Graph ofg (b) Graph of h ________g_~r________ Absolute maximum of g: D Absolute maximum of h: D Absolute minimum of g: D Absolute minimum of h: D The area A (r) (in square meters) of a circular algae colony with radius r meters is given by A (r) = ar-. 13 The radius M (t) (in meters) after t minutes is given by M (t) = 3 t. Write a formula for the area Z (t) (in square meters) of the algae colony after t minutes. It is not necessary to simplify. Z (t) = 1 00 X