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Algebra
A rational function is a function that can be written in the form
f ( x ) = g ( x ) h ( x )
where
h ( x ) ≠ 0
.
The most basic rational function is
f ( x ) = 1 x
, where
x ≠ 0
. This is called the parent rational function.
Use the Desmos
(Links to an external site.)
activity to explore the function
f ( x ) = 1 x
. Take a close look at the table of values as well. Use any noticings to respond to the following questions:
What seems to be happening to the graph as it gets closer to 0 from the left side?
What seems to be happening to the graph as it gets closer to 0 from the right side?
Is the graph always increasing, always decreasing, or a combination of both? Explain how you know.
Where, if anywhere, do you think the graph crosses the y-axis? Explain how you know.
Where, if anywhere, do you think the graph crosses the x-axis? Explain how you know.
f ( x ) = g ( x ) h ( x )
where
h ( x ) ≠ 0
.
The most basic rational function is
f ( x ) = 1 x
, where
x ≠ 0
. This is called the parent rational function.
Use the Desmos
(Links to an external site.)
activity to explore the function
f ( x ) = 1 x
. Take a close look at the table of values as well. Use any noticings to respond to the following questions:
What seems to be happening to the graph as it gets closer to 0 from the left side?
What seems to be happening to the graph as it gets closer to 0 from the right side?
Is the graph always increasing, always decreasing, or a combination of both? Explain how you know.
Where, if anywhere, do you think the graph crosses the y-axis? Explain how you know.
Where, if anywhere, do you think the graph crosses the x-axis? Explain how you know.
Algebra
Provide two rational expressions so that when they are multiplied, they result in an expression with denominator of 1.
Algebra
Consider the expression
x − 4 x − 7
. What is the domain of the numerator? Explain how you know. What is the domain of the denominator? Explain how you know.
Put both parts together to define the domain for the entire expression.
x − 4 x − 7
. What is the domain of the numerator? Explain how you know. What is the domain of the denominator? Explain how you know.
Put both parts together to define the domain for the entire expression.
Algebra
Consider the expression
2 x 3 − 3 x 2 − 17 x − 12
. This expression has the following linear factors:
( x + 1 ) ( x − 4 ) ( 2 x + 3 )
. Which of those factors could not be the divisor when using synthetic division?
2 x 3 − 3 x 2 − 17 x − 12
. This expression has the following linear factors:
( x + 1 ) ( x − 4 ) ( 2 x + 3 )
. Which of those factors could not be the divisor when using synthetic division?
Algebra
For the graph of the function
f ( x ) = − 2 ( x + 1 ) 2 − 4
, determine each of the following and explain how you know:
Whether the graph opens upwards or downwards
The axis of symmetry of the graph
The vertex of the graph
f ( x ) = − 2 ( x + 1 ) 2 − 4
, determine each of the following and explain how you know:
Whether the graph opens upwards or downwards
The axis of symmetry of the graph
The vertex of the graph
Algebra
Find the missing number in the sequence 17,83,92,42,69,?
Algebra
-8x-8y=-8
y=-5
y=-5
Algebra
The import duty on a certain electronic product increased by 20%. the demand for it thereby reduced by 10% is there a percentage increase or decrease in revenue and by how much?
Algebra
The magnitude of the velocity of a particle which moves along the curve x=2 sin ??¡3t,y=2 cos ??¡3t and z=8t at any time t>0 is ?
Algebra
simplify 2/3 if y=6
