Math Questions x5 (Functions and graphs)
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Question 1: (2 points) Evaluate the function:
f(x)=−2.5x2+2x−1
for the given values of x to complete the following table (tabulate all values of f(x) to 2 decimal places):
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Question 2: (2 points) The giant honey bee, Apis dorsata, is an open nesting honey bee found throughout South and Southeast Asia. Apis dorsata workers are approximately twice the size of Apis mellifera workers (the bees used by commercial honey producers). These bees are very dangerous; their stings are capable of penetrating the fabric of two bee suits and they are known to attack in groups.
Like other honey bees, giant honey bees use waggle dances to indicate the locations of forage and potential new homes to their nestmates. Mathematically, the direction to a target resource indicated by a waggle phase of a dance is a function of the angle that a bee dances and the distance to the target is a function of the duration of the waggle phase. Analysis of experimental data [1, 2] suggested the following approximate relationship between the observed waggle phase duration of giant honey bees, t (in seconds), and distance indicated by the waggle phase, d(t) (in metres):
d(t)≈{ 180t + 207.4 for 0 <t ≤ 1.9775 { 394t − 215.48 for t > 1.9775
The durations of individual waggle phases are often quite variable within a dance. From experimental data for the study in [2], a worker produced a dance with 4 circuits with waggle phase durations: 1.19, 3.516, 2.412 and 1.576 seconds. What distance was indicated by each waggle phase (to the nearest metre)?
1.19 seconds indicated an approximate distance of: ____________ (m)
3.516 seconds indicated an approximate distance of: ____________ (m)
2.412 seconds indicated an approximate distance of: ____________ (m)
1.576 seconds indicated an approximate distance of: ____________(m)
A method for determining a best estimate of the distance described by an entire dance is to calculate the mean distance indicated by all dance circuits. What was the average distance indicated by the 4 dance circuits (to the nearest metre)?
Mean distance = ____________ (m). |
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Question 3: (2 points) Identify if the following eight plots represent graphs of functions of x, or not.
Function [ ] Not a function [ ]
Function [ ] Not a function [ ]
Function [ ] Not a function [ ]
Function [ ] Not a function [ ]
Function [ ] Not a function [ ]
Function [ ] Not a function [ ]
Function [ ] Not a function [ ]
Function [ ] Not a function [ ] |
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Question 4: (3 points) Given that f(x)=x2+8x+7 and g(x)=10x+9, determine the following:
f(x)+g(x)= __________
f(x)−g(x)= __________
g(x)−f(x)= __________
f(x)g(x)= __________
f(g(x))= __________
g(f(x))= __________ |
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Question 5: (1 point) Determine the inverse function of f(x)=−x+1.
f−1(x)= __________.
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