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MAT111A - College Algebra Homework Problems

   

Added on  2020-03-04

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Question OneA function is a relation in which each element of the domain is paired with exactly one element of the range. DomainRange456788Since each element of the domain is paired with exactly one element of the range, the relation is a function. Question TwoThe graph of g is a shifted graph of f, two steps upwards. Question Threeyisafunctionofx.Iusedthedescriptionofdomain−rangerelation¿confirm.A function is a relation in which each element of the domain is paired with exactly one element of the range; as illustrated below: domainRange-11-22-33-44
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Question Foura)a. the function’s domain: −∞<x<∞b)b. the function’s range: 1≤y≤∞c)c. the x-intercepts, if any:¿d)d. the y-intercept, if any: d=1e)e. the function’s values f(−1)and f(3)f(−1)=2f(3)=4Question Fivea) The intervals on which the function is increasing, if any:Thefunctionisincreasing∈theineterval:−∞≤x<−1b) The intervals on which the function is decreasing, if any:Thefunctionisdecreasing∈theinterval:−1<x≤∞c)The intervals on which the function is constant, if any: Thefunctionisconstantatx=−1Question SixThe graph is a graph of odd function. The graph is symmetrical based on the origin. As illustrated by: (−1,1),(0,0),(1,−1)Question Sevena)The domain of f: −∞≤x≤∞b)The range of f:4≤f(x)≤∞c)The x-intercepts :¿1d)The y-intercept: ¿4e)Intervals on which f is increasing: 4<x≤∞f)Intervals on which f is decreasing :0<x<4g)Intervals on which f is constant :−∞≤x≤0h)The number at which f has a relative minimum: x=4i)The relative minimum of f:f(x)=−4j)f(-3) :¿4k)The values of x for which f(x) = -2 :x=2l)is f even, odd, or neither?: NeitherQuestion Eight
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a)Increasing : 25≤Age<55Decreasing: 55<Age≤75b)The percentage of body fat in women reach maximum at age 55. At age 55, the percentage of body fat is 38%. Question NineThe slope/gradient, m, of a line is the rate of change in y in relation to x. m=y2−y1x2−x1=2−12+2=14Since the gradient of the line through the points has a positive value, the line rises. Question TenThe point slope form of an equation is given by: y−k=m(x−h);where(h,k)isapointontheline∧misthegradientoftheline.¿thiscase,m=−2,h=0∧k=−3Thus the point-slope form of the equation will be given by: y−(−3)=−2(x−0);Which is simplified to:y+3=−2x;On the other hand, The slope-intercept form of an equation is given by:y=mx+c;wheremisthegradient∧cistheyintercept;¿thiscasem=−2,c=−3
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