one to-one function (math 11)

PERFORMANCE TASK

INMATH

ONE-TO-ONE FUNCTION

• A function for which every element of the range of the function corresponds to exactly one element of the domain. One-to-one is often written 1-1.

• NOTE: y = f(x) is a function if it passes the vertical line test and the horizontal line test.

GRAPHING ONE-TO-ONE FUNCTION

• Construct a table of values. Simply choose a number for x

• Solve for the corresponding value of y.• Plot the points on the graph.• Connect the points.

INVERSE FUNCTION

• The function obtained by switching the x and y variables in a function. The inverse of function f is written f^(-1)

• NOTE: The new relation obtained by reversing the x and y values of a function is not necessarily a function itself. The new relation is only a function if the original function is one-to-one function.

Finding the inverse• Change f (x) to y• Interchange x and

y• Solve y In terms of

x• Change y to f^(-1)

Graphing inverse function

• Get first the inverse of the given function.• Construct a table of values. Simply choose a number

for x.• Solve the corresponding value of y.• Plot the points on the graph.• Connect the points.

Significant Application of One-to-One Function and Inverse

Function

• GPS or Global Positioning System

• Concert Sears and Tickets• Make-up of DNA molecules

• Temperature conversion• Elements in the Periodic Table• Dewey decimals system• Birthdays

Both are significant because they both help interpret various phenomena around us. These types of functions make sense when we grew up and know the true value of money. They are significant because it helps us to understand the meaning of what life is. It is said that these functions reciprocates one another and that no matter how try to change it both are still related, like the measurements we see in skyscrapers and various infrastructure.

It also allows us to understand the weather and that in every part of the globe there is a specific type of weather or climate being experienced. These functions are significant for they help us navigate our own future and what lies before us it the result of what we do today.

Mathematicians• Gottfried Leibniz – introduced the term “function” to

describe a quantity related to a curve.• Johann Bernoulli – started calling expressions made of a

single variable “functions” to 1698 he agreed with Leibniz that any quantity formed may be called a function of x.

• Leonhard Euler – said that the function of a variable quantity is an analytic expression compose In anyway whatsoever of the variable quantity and numbers or constant quantities.

• Jean – Baptiste Joseph Fourier – claimed that an arbitrary function could be represented by a Fourier series. He said that functions were neither continuous nor not defined by an analytic expression.

• Augustin – Louis Cauchy – he said that a function is being defined by an analytic expression or by an equation or a system of equation. He differs from his predecessors.

• Nikolai Lobachevsky – said that the general concept of a function requires that a function of x be defined as number given for each x and varying gradually with x.

• Johann Peter Gustav Lejeunne Dirichlet – said that y corresponds to each x, and more over in such a way that when x ranges continuously over the interval a to b then y is called a continuous function of x for this interval.

• Godfrey Harold “G.H.” Hardy – defined a function as a relation between two variables x and y such that “to some values of x at any rate correspond values of y”

Finding the DomainSolve the equation for y in terms of x• If y is polynomial, the domain is the set of real numbers.• If y is a rational expression and contains an expression

d(s) in the denominator, the domain is the set of real numbers except those values of x that make the denominator equal to zero.

• If y contains a radical expression, where n is an event natural numbers, the domain is a set of real numbers, except those values of x that made r(x) less than zero.

Finding the Range

Solve the equation for x in terms of y• If x is polynomial, the domain is the set of real numbers.• If x is a rational expression and contains an expression

d(s) in the denominator, the domain is the set of real numbers except those values of x that make the denominator equal to zero.

• If x contains a radical expression, where n is an event natural numbers, the domain is a set of real numbers, except those values of x that made r(y) less than zero.

PROBLEMS

S.T.A.R. Laboratories conducted a research to see how fast horses can grow from birth to its first 5 months . The team uses the equation, f(x) = 15x + 10kg. How much weight can the horses have every month?

Solution*

Let x be represented as months:

• (1) = 15(1) + 10= 15 + 10

= 25

• (3) = 15(3) + 10= 45 + 10

= 55• (2) = 15(2) + 10= 30 + 10

= 40

• f(x) = 15(x) + 10

• (4) = 15(4) + 10= 60 + 10

= 70

• (5) = 15(5) + 10= 75 + 10

= 85

The horses would weigh, 25Kg, 40Kg, 55Kg, 70Kg, and 85Kg In span of 5 months.

Stephen missed the mid-term exam because of a flu. The normal body of human is 37° C. However, Stephen recorded 3 different readings in a span of 3 days. On the first day, his temperature was 37.9 °C, It increased to 38.6 °C by the second day and it reached 39.2 °C on the third day. What would be Stephen’s temperature readings if it were in Fahrenheit Scale?

oFunction Rule:°F = 1.8(°C) + 32

• F(37.9°C) = 1.8(37.9°C) + 32

= 68.22 + 32

= 100.22 °F

• F(38.6°C) = 1.8(38.6°C) + 32

= 69.48 + 32

= 101.48 °F

• F(39.2°C) = 1.8(39.2°C) + 32

= 70.56 + 32

= 102.56 °F

Stephen’s temperature readings in Fahrenheit are 100.22°F, 101. 48°F , 102.56°F.

... End

GROUP 4(11 – Kindness)

• Sombilon• Olden• Odulio• Dawal• Sohal