Questions on Functions with Solutio

Questions on Functions with Solutions

Several questions on functions are presented and their detailed solutions discussed. The questions cover a wide range of concepts related to functions such as definition, domain, range, evaluation, composition and transformations of the graphs of functions.

Question 1: Is the graph shown below that of a function?

graph of question 1
Solution to Question 1:

Vertical line test: A vertcal line at x = 0 for example cuts the graph at two points. The graph is not that of a function.
Question 2: Does the equation

y 2 + x = 1


represents a function y in terms of x?
Solution to Question 2:

Solve the above equation for y

y 2= 1 - x

y = + SQRT(1 - x) or y = - SQRT(1 - x)


For one value of x we have two values of y and this is not a function.
Question 3: Function f is defined by

f(x) = - 2 x 2 + 6 x - 3


find f(- 2).
Solution to Question 3:

Substitute x by -2 in the formula of the function and calculate f(-2) as follows

f(-2) = - 2 (-2) 2 + 6 (-2) - 3

f(-2) = -23
Question 4: Function h is defined by

h(x) = 3 x 2 - 7 x - 5


find h(x - 2).
Solution to Question 4:

Substitute x by x - 2 in the formula of function h

h(x - 2) = 3 (x - 2) 2 - 7 (x - 2) - 5

Expand and group like terms

h(x - 2) = 3 ( x 2 - 4 x + 4 ) - 7 x + 14 - 5

= 3 x 2 - 19 x + 7
Question 5: Functions f and g are defined by

f(x) = - 7 x - 5 and g(x) = 10 x - 12

ผลลัพธ์ (อังกฤษ) 2:

Functions with questions on Solutions Presented Several questions on functions are detailed and their Solutions discussed. The questions Cover a Wide Range of Concepts related to functions such as Definition, DOMAIN, Range, evaluation, composition and transformations of the graphs of functions. Question 1: Is the graph shown Below that of a function? Graph of question 1 Solution to Question. 1: Vertical Test line: A line at x = 0 Vertcal for example Cuts Two points at the graph. The graph is not that of a function. Question 2: Does the Equation Y 2 + x = 1 represents a function Y in terms of x? Solution to Question 2: Solve the above Equation for Y Y 2 = 1 - x Y = +. SQRT (1 - x) or Y = - SQRT (1 - x) For one VALUE of x we have Two values ​​of Y and this is not a function. Question 3: function F is defined by F (x) = - 2 x. 2 x 6 + - 3 Find F (- 2). Solution to Question 3: Substitute x by -2 in the Formula of the Calculate function and F (-2) as follows F (-2) = - 2 (-2). 6 + 2 (-2) - 3 F (-2) = -23 Question 4: Function H is defined by H (x) = 3 x 2 - x 7 - 5 Find H (x - 2). Solution to Question 4. : Substitute x by x - 2 in the Formula of function H H (x - 2) = 3 (x - 2) 2 - 7 (x - 2) - 5 Expand and Group like terms H (x - 2) = 3 (. x 2 - 4 x + 4) - 7 x + 14 - 5 = 3 x 2 - 19 x + 7 Question 5: Functions F and G are defined by F (x) = - 7 x - 5 and G (x) =. 10 x - 12