Mathematics
MHF4U: ASSIGNMENT – 1
· Yes it is a function, the domain is (-∞,∞) and range is (-∞,∞)
· No it is not a function, the domain is (-3,3) and range is (-3,3)
· Yes it is a function, the domain is (-∞,5] and range is [0,∞)
· Yes it is a function, the domain is (-∞,∞) and range is [2,∞)
Stretching f(x) vertically by a factor of 3 will result to.
Reflection in x axis and shifted to the right 5 units
The resulted equation is:
Replace x with y and solve for y.
Inverse of the f(x) is:
Replace x with y and solve for y.
Inverse of the b(x) is:
Replace x with y and solve for y.
Inverse of the g(x) is:
Replace x with y and solve for y.
Inverse of the g(x) is:
4. (10 marks) The fish population, in thousands, in a lake at any time, x, in years is modelled by the following functions:
a) Graph
b) From the graph we can see that function is not continuous at x=6, else it is continuous.
Thus 64-32=32 fishes killed by chemical spill
d) 4x+8=32 when x=6 and 4x+8=64 when x=14
So the difference is 14-6=8
Thus at year 14 population recover.
· The function is discontinues are become negative when time (x) become less then 0
y=(x +3)2 The graph shifts 3 units to the left.
y=-(x +3)2 The graph is reflected over the x-axis.
y=−(x +3)2 −2 The graph is shifted 2 units down.
Rate of change everywhere
· At x=-2 f'(-2)=12(-2)=-24
· At x=0 f'(0)=12(0)=0
· At x=4 f'(4)=12(4)=48
· At x=8 f'(8)=12(8)=96
· The average rate of change is equal but in opposite site. The instantaneous rate of height will be zero at the midpoint at t=2
The minimum point is (-5,-40)
· Tangent line at x=-5
Compute the slope:
Y=mx+b
0(-5)+b=-40
so b=-40
· The tangent line is passes through under the point
·
· Graph of the function.
The maximum point is (7.5,184.75)
· Tangent line at x=7.5
Compute the slope:
Y=mx+b
184.75=0(7.5)+b
184.75=b
· The tangent line is passes through over the point
· Graph of the function.
The minimum point is (3.25,-45.25)
· Tangent line at x=3.25
Compute the slope:
Y=mx+b
-45.25=0(3.5)+b
-45.25=b
· The tangent line is passes through under the point
· Graph of the function.
The maximum point is (6,18.45)
· Tangent line at x=6
Compute the slope:
Y=mx+b
18.45=0(6)+b
18.45=b
· The tangent line is passes through under the point