i) Which functions are polynomial functions? Justify your answer.
ii) State the degree and the leading coefficient of each polynomial function.
a) f(x) = 3x^2 -5x + 1
b) g(x) = x(4-x)
c) h(x) = 3x + 2x
d) m(x) = x^{-2}
e) r(x) = 5(x -1)^3
For the graph, do the following..
For the graph, do the following..
Assign the following functions for below:
\displaystyle
\begin{array}{llll}
&y=-x^5, y = \frac{2}{3}x^4, y= 4x^3, y = 0.2x^6 \\
\end{array}
a) Extends from quadrant 3 to quadrant 1
b) Extends from quadrant 2 to quadrant 4
c) Extends from quadrant 2 to quadrant 1
d) Extends from quadrant 3 to quadrant 4
Assign the following functions for below:
\displaystyle
\begin{array}{llll}
&g(x) = 0.5x^4 -3x^2 + 5x \\
&h(x) = x^5 -7x^3 + 2x -3\\
&p(x) = -x^6 + 5x^3 + 4
\end{array}
For each polynomial function below
\displaystyle
\begin{array}{llll}
&g(x) = 0.5x^4 -3x^2 + 5x \\
&h(x) = x^5 -7x^3 + 2x -3\\
&p(x) = -x^6 + 5x^3 + 4
\end{array}
a) Determine which finite differences are constant.
b) Find the value of the constant finite differences.
c) Identify the type of symmetry, if it exists.
a) State the degree of the polynomial function that corresponds to each constant finite difference.
b) Determine the value of the leading coefficient of each polynomial function in part a).
Each table of values represents a polynomial function. Use finite differences to determine the following for each.
Each table of values represents a polynomial function. Use finite differences to determine the following for each.
A parachutist jumps from a plane 3500 m above the ground. The height, h
, in metres, of the parachutist above the ground t seconds after the jump can be modelled by the function h(t) = 3500 -4.9t^2
a) What type of function is h(t)?
b) Without calculating the finite differences, determine
c) Describe the end behaviour of this function assuming there are no restrictions on the domain.
d) Graph the function. State any reasonable restrictions on the domain.
e) What do the t
—intercepts of the graph represent for this situation?
Use each graph of a polynomial function to determine
Use each graph of a polynomial function to determine
Sketch a graph of the polynomial function.
y = (x+ 1)(x -3)(x + 2)
Sketch a graph of the polynomial function.
y = -x(x + 1)(x+2)^2
Sketch a graph of the polynomial function.
y = (x - 4)^2(x+3)^3
The zeros of a quartic function are -3, -1
, and 2
(order 2). Determine
a) equations for two functions that satisfy this condition
b) an equation for a function that satisfies this condition and passes through the point (1, 4).
Without graphing, determine if the polynomial function has line symmetry about the y-axis, point symmetry about the origin, or neither. Graph the functions to verify your answers.
\displaystyle
f(x) = -x^5 . +7x^3 + 2x
Without graphing, determine if the polynomial function has line symmetry about the y-axis, point symmetry about the origin, or neither. Graph the functions to verify your answers.
\displaystyle
f(x) = x^4 + 3x^2 +1
Without graphing, determine if the polynomial function has line symmetry about the y-axis, point symmetry about the origin, or neither. Graph the functions to verify your answers.
\displaystyle
f(x) = 4x^3 -3x^2 + 8x + 1
Determine an equation for the polynomial function that corresponds to each graph.
Determine an equation for the polynomial function that corresponds to each graph.
f(x)
, to obtain the transformed function. Then, write the corresponding equation.\displaystyle
f(x) =x^3, y = -\frac{1}{4}f(x) -2
f(x)
, to obtain the transformed function. Then, write the corresponding equation.\displaystyle
f(x) =x^4, y = 5f[\frac{2}{5}(x -3)] + 1
f(x) =x^4
is compressed vertically by a factor of \frac{3}{5}
, stretched horizontally by a factor of 2
, reflected in the y-axis, and translated 1 unit up and 4 units to the left.
f(x) =x^4
is compressed vertically by a factor of \frac{3}{5}
, stretched horizontally by a factor of 2, reflected in the y-axis, and translated 1 unit up and 4 units to the left.
Which are not examples of average rates of change? Explain why.
a) The average height of the players on the basketball team is 2.1 m.
b) The temperature of water in the pool decreased by 5°C over 3 days.
c) The snowboarder raced across the finish line at 60 km/h.
d) The class average on the last math test was 75%.
e) The value of the Canadian dollar increased from $0.75 U.S. to $1.01 U.S. in 8 months.
f) Approximately 30 cm of snow fell over a 5-h period.
The graph represents the approximate value of a stock over 1 year.
a) What was the value of the stock at the start of the year? at the end of the year?
b) What does the graph tell you about the average rate of change of the value of the stock in each interval?
The table shows the percent of Canadian households that used the Internet for electronic banking.
a) Determine the average rate of change, in percent, of households that used the Internet for electronic banking from 1999 to 2003.
b) Estimate the instantaneous rate of change in the percent of households that used the Internet for electronic banking in the year 2000, and also in 2002.
c) Compare the values you found in parts a) and b). Explain any similarities and differences.