How is the graph of y=log(x) transformed to produce the graph of y=log(2x)+3

Mathematics

1 answer:

V125BC [204]3 years ago

6 0

Answer:

horizontally compressed by a factor of 2 and translated upward by 3 units.

Step-by-step explanation:

A multiplier of x in a function transformation is effectively a compression factor. That is f(2x) will have half the horizontal extent of f(x) for the same values of x.

Addition of a constant the the value of a function effectively translates the graph upward by that amount. The graph of y = log(2x) +3 has been translated upward 3 units.

The graph of y=log(x) has been horizontally compressed and translated upward to produce the graph of y = log(2x) +3.

You might be interested in

Is the relationship shown by the data linear? If so, model the data with an equation.

zhenek [66]

Answer:

Therefore the equation of the line through ( -7 , 5 ) and ( -5 , 9) is

Linear Relationship i.e $y-5=2(x+7)$

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( -7, 5 )

point B( x₂ , y₂) ≡ (-5, 9)

To Find:

Equation of Line AB =?

Solution:

Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula

$(y - y_{1} )=(\frac{y_{2}-y_{1} }{x_{2}-x_{1} })\times(x-x_{1}) \\$

Substituting the given values in a above equation we get

$(y-(5))=(\frac{9-(5)}{-5--7})\times (x--7)\\ \\(y-5)=\frac{4}{2}(x+7)\\\\y-5=2(x+7)...............\textrm{which is the required equation of the line AB}$