Math 1A Practice Test 2 Math 1A Practice Test 2 1. Consider the graph of y= f(x)

Question

Math 1A Practice Test 2 Math 1A Practice Test 2 1. Consider the graph of y= f(x) shown. (No explanation is required) a) State the equation of a horizontal asymptote of fix) b) State all values of x at which fix) is c) State the intervals on which fix) is differentiable (comma separated list) d) State the intervals on which fix)ko (comma separated list) e) State the intervals on which f(x)>0 (comma separated list) not differentiable y-fx) f State the values of x for which (x)-0 het of a cold vam placed in a hot oven is aiven by

Explanation / Answer

a)A horizontal asymptote for a function is a horizontal line that the graph of the function approaches as xapproaches ? (infinity) or -? (minus infinity).

y = -2 (as x? -?)

b) f(x) is not differentiable means either the function is discontinous at some point or it takes a sharp curve

we have two points where the function is not differentiable

x=0,-4

c) f(x) is differentiable in (-?,-4) and (-4,0) and (0,?)

d)f'(x) < 0 means the interval in which f(x) is decreasing

means we have (-4,0) and (2,?)

e) f'(x) < 0 means the interval in which f(x) is increasing

means we have (-?,-4) and (0,2)

f). f'(x)=0 means where the slope is 0 or the point where the tangent is parallel to x-axis

in our case we have x=2

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