Is the following statement true or false?
Is the following statement true or false?
Is the following statement true or false?
f(x) = \frac{3}{x - 2}, x
can be any real number except x = 2
.Is the following statement true or false?
\sqrt{81}
can be fully simplified to 3 \sqrt{9}
.Is the following statement true or false?
A quadratic function and a linear function always intersect at least once.
A vertical line test can be used to determine
A If a relation is a function
B if a relation is constant
C if a function is relation
D all of the above are true.
The range of the function f(x)= -x^2 + 7
is
A \{y \in \mathbb{R}, y \geq 7\}
B \{y \in \mathbb{R}, y \leq 7\}
C \{y \in \mathbb{R}, y > 0\}
D \{y \in \mathbb{R}
Which function would produce an output of y = 9
for x = 1
and for x = - 1
.
A y = 2x + 7
B y = x^2 -3x + 1
C y = 2x^2 + 7
D All of the above
The vertex of y = -3x^2 + 6x -2
is
\displaystyle
\begin{array}{llll}
&A) &(1, -2) & &B) & (1, 1) \\
&C) & (-1, 1) & &D) &(-1, -2) \\
\end{array}
Given f(x) =x^2-6x + 10
, if f(a) = 1
, what is the value of a
?
\displaystyle
\begin{array}{llll}
&A) &5 & &B) & 3 \\
&C) & 2 & &D) &1 \\
\end{array}
Sketch a relation that is
a) a function with domain \{x \in \mathbb{R}\}
and range \{y \in \mathbb{R}, -5 \leq y \leq 5\}
.
b) not a function with domain \{x\in \mathbb{R}, -5\leq x \leq 5\}
and range \{y \in \mathbb{R}, -5 \leq y \leq 5\}
State the domain and the range of each function.
State the domain and the range of each function.
The time needed for a pendulum to make one complete swing is called the period of the pendulum. The period, T
, in seconds, for a pendulum of length l
, in meters, can be approximated using the function T = 2\sqrt{l}
.
a) State the domain and the range of T
.
b) Sketch a graph of the relation.
c) Is the relation a function? Explain.
Write the ordered pairs that correspond to the mapping diagram. Is this a function?
a) Find the vertex of the parabola defined by f(x) = -\frac{1}{2}x^2 + 4x + 3
b) Is the vertex a minimum or a maximum? Explain.
c) How many x-intercepts does the function have? Explain.
Pat has 30 m
of fencing to enclose three identical stalls behind the barn, as shown.
a) What dimensions will produce a maximum area for each stall?
b) What it that maximum area of each stall?
Simon knows that at \$ 30
per ticket, 500 tickets to a show will be sold. He also knows that for every \$1
increase in price, 10 fewer tickets will be sold.
a) Model the revenue as a quartic function.
b) What ticket price will maximize revenue?
c) What is the maximum revenue?
Prefer each radical multiplication and simplify where possible.
3\sqrt{2}(2\sqrt{3} -3\sqrt{2})
Prefer each radical multiplication and simplify where possible.
(\sqrt{2} + x)(\sqrt{2} - x)
For what value of x
is \sqrt{x} + \sqrt{x} = \sqrt{x} \times \sqrt{x}
, where x > 0
?
Justify your answer.
Consider the quadratic function f(x) = -\frac{1}{2}x^2 + 4x + 10
.
a) Find the x-intercepts.
b) Use two methods to fid the vertex.
c) Sketch a graph of the function.
A rectangle has a length that is 3
m more than twice the width. If the total area is 65 m^2
, find the dimensions of the rectangle.
Find the equation, in standard form, of the quadratic function that has x-intercepts -5 \pm \sqrt{3}
and passes through the point (-3, 8)
.
The graph of a quartic function is given
a) Find the equation of the function.
b) Find the maximum value of the function.
Find the point(s) of intersection of y = -x^2 + 5x + 8
and y= 2x- 10
.
a) Compare the graphs of f(x) = 3x^2 -4
and g(x) = 3(x - 2)(x+ 2)
b) What needs to be changed in the equation for f(x)
to make the tow functions part of the same family of curves with the same x-intercepts? Explain.
c) Describe the family of curves, in factored form, that has the same x-intercepts as h(x) = 5x^2 -7
.
A baseball is travelling on a path given by the equation y = -0.011x^2 + 1.15x + 1.22
. The profile of the bleachers in the outfield can be modelled with the equation y = 0.6x -72
. All distances are in metres. Does the ball reach the bleachers for a home run? Justify your answer.