Consider the function:

f(x)=5x−4+2\displaystyle {f{{\left({x}\right)}}}=\frac{{5}}{{{x}-{4}}}+{2}

Question 1

Calculate the coordinates of the y\displaystyle {y}-intercept of f\displaystyle {f}.

(\displaystyle {(},\displaystyle ,)\displaystyle {)}    

(2)



Question 2

Calculate the coordinates of the x\displaystyle {x}-intercept of f\displaystyle {f}. 

(\displaystyle {(},\displaystyle ,)\displaystyle {)}    

(3)



Question 3

Sketch the asymptotes and the intercepts with the axes

12345678-1-2-3-4-5-6-7-812345678-1-2-3-4-5-6-7-8
Clear All Draw: LineDot

and select the correct shape of the graph.








(4)



Question 4

For which values of x\displaystyle {x} is f(x)≥0\displaystyle {f{{\left({x}\right)}}}\ge{0}? 

 

(2)



Question 5

Calculate the average rate of change from x=−2\displaystyle {x}=-{2} and x=−3\displaystyle {x}=-{3} . The formula is f(x2)−f(x1)x2−x1\displaystyle \frac{{{f{{\left({x}_{{2}}\right)}}}-{f{{\left({x}_{{1}}\right)}}}}}{{{x}_{{2}}-{x}_{{1}}}} 

Average rate of change =\displaystyle =  

(4)



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