Wendy purchases a chalkboard priced at $76. With sales tax, the total comes out to $82.84.
1 answer:
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Answer:
- Inverse Variation
- Equation:
Step-by-step explanation:
Given
X-> 2 | 4 | 8 | 12
Y-> 6 | 3 | 3/2 | 1
Required
- State the type of variation the table represents
- Determine the equation to model the data
To check for type of variation; we'll make use of trial by error method.
To start with; We'll check for direct variation.
This is done using the following expression;
where k is the constant of variation
Make k the subject of formula
When Y = 6, X= 2
When Y = 3, X = 4
There's no need to check further as both values of k are not equal
To check for inverse variation;
Make k the subject of formula
When Y = 6, X= 2
When Y = 3, X = 4
When Y = 3/2; X = 8
When Y = 1, X = 12
Note that for all values of X and Y, K remains constant;
Hence, the table represents an inverse direction
To determine the equation;
We make use of
Substitute 12 for k
So, the equation becomes
Reorder
Hence, the equation is
Given:
The parent function is
Consider the transformed function is g(x) instead of f(x) because both functions are different.
Step-by-step explanation:
We have,
It can be written as
...(i)
The translation is defined as
.... (ii)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<|k|<1, then the graph compressed vertically by factor k and if |k|>1, then the graph stretch vertically by factor k.
If k is negative, then f(x) is reflected across the x-axis to get g(x).
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (i) and (ii), we get
, f(x) shifts 4 units right.
, f(x) shifts 8 units down.
, it is negative so f(x) reflected across the x-axis.
, so f(x) stretched vertically by factor 5.
Therefore, the function f(x) reflected across the x-axis, stretched vertically by factor 5 and shifted 4 units right 8 units down to get g(x).
Answer:
Step-by-step explanation:
We need to factor out numerator and denominator in order to simplify the rational expression by cancelling common factors.
Numerator : x^3 - 4 x = x (x^2 - 4) = x (x - 2) (x + 2)
Denominator (factoring by grouping):
x^2 - 5 x + 6 = x^2 - 3 x - 2 x + 6 = x (x - 3) - 2 (x - 3) = (x - 3) (x - 2)
Then we can cancel out the common factor (x - 2) in both numerator and denominator, leading to:
x (x + 2) / (x - 3) = (x^2 + 2)/ (x-3)