REGIONAL DIAGNOSTIC TEST - GENERAL MATHEMATICS

Functions offer an interesting way to understand relationships between quantities. As a businessman, Mr. Cruz uses functions to predict the income of his store located in Balanga City. He used previous data to make models that could describe the relationship between number of customer (x) and the sales for each of his products. For product A, the income is represented by A(x)=420x-250, while the income for product B is given by B(x)=250x + 35.

Which of the following would be an example of a function?

If y=f(x), which of the following CANNOT be true?

Mr. Cruz bought a box of product D with a total cost of x pesos. If there are 13 pieces of product D inside the box, which would give the function for the price of each piece?

If in a certain day, Mr. Cruz was able to sell 20 pieces of product A, what was the sales for product A that day? 

Suppose you are working for Mr Cruz and a customer wants to buy 5 pieces of product B. How would you determine the total price of the purchase?

Mr. Cruz told you that the price of product D is the composition of the functions A(x) and B(x) wherein the function A is applied to the results of the function of B. How would this be expressed mathematically?

What is the value of (𝐵 ○ 𝐴)(2)?

For product C, Mr Cruz determines that the function C(x) can be found by multiplying the number of customers by P120. Which of the following represents the function C?

How much will be the total sales from product A and B in a certain period of time?

During the celebration of the Philippine Independence Day on June 12, 2021, the store had a record high in terms of both number of customers and sales. If on that day, the store received 200 customers, what was the total sales for Product A?

RATIONAL FUNCTIONS.

We can simply say that a rational function can be defined by a rational fraction wherein both numerator and denominator are polynomial functions. As an artist, Ms Dilao takes interest on the ratio of the sides of a rectangular canvas. She believes that this ratio could highlight the beauty of a painting. In one of her collections, she used different rectangular canvas following the function L(x)=5x+8 for the length and W(x)=4x-2.

Which represents the ratio of the length to the width of the rectangular canvas?

Suppose the ratio . 4𝑥−2 is equal to ½. What is x?

                                            5𝑥+8

In one of her exhibits, the ratio of the sides of the canvas is given by 𝑓(𝑥) = 2𝑥+1. What is the domain of the rational 𝑥−2 function?

What is the x- intercept of the graph of 𝑓(𝑥) = 2𝑥+1?

                                                                                                           𝑥−2

Which of the following is the y-intercept of the graph of the rational function 𝑓(𝑥) = 2𝑥+1?

                                                                                                                                                                                                 𝑥−2