18. Find the domain of the function [tex] \displaystyle f(x) = x^2 -1 [/tex]:
Answer: [tex] \displaystyle \textsf{D. All set of real numbers} [/tex]
Solution: Any real number we substitute in the function [tex]\displaystyle f(x) = x^2 -1[/tex] maps to a set of values, such that it does not give an undefined value or does not contain holes in the graph.
19. It is a function that has a degree of one and can be written in a slope-intercept form.
Answer: [tex] \displaystyle \textsf{B. Linear Function} [/tex]
Solution: Linear function can be represented in the form of , where is the slope, and is the y-intercept of the line.
20. What is the graph of a linear function?
Answer: [tex] \displaystyle \textsf{A. straight line} [/tex]
Solution: A linear function or a linear equation has a graph of a straight line.
21. Which of the following equation represents a linear function?
Answer: [tex] \displaystyle \textsf{A.\ }f(x)=6x-3 [/tex]
Solution: All of the choices, except for function in letter A, are quadratic equations. Quadratic functions, when simplified, are in the form of , where .
22. What is the value of the function [tex] \displaystyle f(x)=5x-2 [/tex] at [tex] \displaystyle x=3 [/tex]?
Answer: [tex] \displaystyle \textsf{D. 13} [/tex]
Solution: We can evaluate the function by substituting 3 in the function:
[tex] \displaystyle f(x)=5x-2 [/tex]
[tex] \displaystyle f(3)=5(3)-2 [/tex]
[tex] \displaystyle f(3)=15-2 [/tex]
[tex] \displaystyle \boxed{f(3)=13} [/tex]
23. What is the equivalent equation of [tex] \displaystyle 6x+3y=9 [/tex]?
Answer: [tex] \displaystyle \textsf{D.\ }y= -2x + 3 [/tex]
Solution: We simplify the equation as follows:
[tex] \displaystyle 6x+3y=9 [/tex]
[tex] \displaystyle 3y= -6x + 9 [/tex]
[tex] \displaystyle 3y/3= -6x/3 + 9/3 [/tex]
[tex]\displaystyle \boxed{y= -2x + 3}[/tex]
24. What is the equation of a line in the form of [tex] \displaystyle y=mx+b [/tex] whose slope is [tex] \displaystyle 5 [/tex] and passes through the point [tex] \displaystyle (1,2) [/tex]?
Answer: [tex] \displaystyle \textsf{D.\ }y = 5x-3 [/tex]
Solution: We use the point-slope form to find the line equation:
[tex] \displaystyle y-y_1 = m(x-x_1) [/tex]
[tex] \displaystyle y-2 = 5(x-1) [/tex]
[tex] \displaystyle y-2 = 5x-5 [/tex]
[tex] \displaystyle y = 5x-5+2 [/tex]
[tex] \displaystyle \boxed{y = 5x-3} [/tex]
25. A computer game service charges Php 13 for the first one hour and Php 10 for every additional hour thereof. How much will a player pay if his game lasts for 6 hours?
Answer: [tex]\displaystyle \textsf{A.\ }y = 10x+13\textsf{\ ,Php. 73}[/tex]
Solution: We make an equation base on the problem, and evaluate it afterwards:
Php. 13 is the y-intercept,
Php. 10 is the slope:
[tex] \displaystyle y = mx+b [/tex]
[tex]\displaystyle \boxed{y = 10x+13}[/tex]
Substitute 6:
[tex] \displaystyle y = 10(6)+13 [/tex]
[tex] \displaystyle y = 60+13 [/tex]
[tex]\displaystyle \boxed{y = 73}[/tex]
26. In Mathematics, what do you call the statement composed of 2 clauses, the "If and then clauses"?
Answer: [tex] \displaystyle \textsf{B.\ conditional statement} [/tex]
Solution: Conditional statements are in the form of "If and then" clauses.
27. In the statement "if p then q", what do you call the p statement?
Answer: [tex] \displaystyle \textsf{D.\ Hypothesis} [/tex]
Solution: In "if p then q", p is the hypothesis, and q is the conclusion.
28. What is the If-Then form of the statement, "Perpendicular lines intersect at a right angle."?
Answer: [tex] \displaystyle \textsf{B.\ If two lines are perpendicular, then they intersect at a right angle.} [/tex]
Solution: We transform "Perpendicular lines intersect at a right angle." into "If two lines are perpendicular, then they intersect at a right angle.", by following the form "if p then q".