Questions

1. Question 1

   Find the point of intersection of the coordinate axes and the following linear functions graphically:

   (i)

   $y=-5x+10$

   (ii)

   $y=2x-1$

   (iii)

   $y=\dfrac{1}{2}x-3$

   (iv)

   $y=3x+\dfrac{3}{2}$

   SolutionTheory
2. Question 2

   Find the point(s) of intersection of the following functions graphically:

   (i)

   $f(x)=2x+5,\; g(x)=-x+5$

   (ii)

   $f(x)=3x-2,\; g(x)=10-x$

   (iii)

   $f(x)=2x-4,\; g(x)=3x-1$

   (iv)

   $f(x)=-3x-4,\; g(x)=\dfrac{1}{2}x+3$

   (v)

   $f(x)=x-1,\; g(x)=x^2-4x+3$

   (vi)

   $f(x)=3x+4,\; g(x)=x^2+2x-8$

   (vii)

   $f(x)=-2x-1,\; g(x)=x^2-4x$

   (viii)

   $f(x)=-x^2-3x+2,\; g(x)=x+6$

   SolutionTheory
3. Question 3

   Graph the following functions:

   (i)

   $y=\sqrt{3x}$

   (ii)

   $y=\sqrt{x}+5$

   (iii)

   $y=-\dfrac{1}{2}\sqrt{x}$

   (iv)

   $y=-\sqrt{x+1}+2$

   (v)

   $y=\sqrt[3]{2x+1}$

   (vi)

   $y=2\sqrt[3]{x}-3$

   (vii)

   $y=\sqrt[3]{x^2+x-2}$

   SolutionTheory
4. Question 4

   A building's height over time is modeled by $H(t)=100+20t$ (metres) where $t$ is the time in months. The height of a growing tree nearby is given by $T(t)=50+10t+t^2$.

   (i)

   At what time will the building and tree have the same height?

   (ii)

   What will that height be?

   SolutionTheory
5. Question 5

   A radioactive substance has a half-life ($t_{1/2}$) of 2 years. If the initial quantity $Q_0$ is 200 grams and the exponential decay function is $Q(t)=Q_0\left(\dfrac{1}{2}\right)^{t/2}$, then find the remaining quantity after 6 years graphically.

   SolutionTheory