DSAT extra practice Ch2 Lv1

The cost of a personal workshop rental in a village is $50, plus $7 per hour the personal workshop is rented. If a personal workshop is rented for [math]x[/math] hours, which of the following functions [math]f[/math] represents the total cost in dollars to rent the personal workshop?

The president of a school had 120 teachers in 2023. He plans to terminate 8 teachers within 3 years. Let [math]x[/math] be the number of years after 2023 and [math]y[/math] be the number of teachers in the school. If [math]y=mx+b[/math] where [math]m[/math] and [math]b[/math] are constants, what is the value of [math]b[/math]?

There are 100 people in a refugee camp. Their daily food is 220 rice balls. Let [math]x[/math] be the number of adults and [math]y[/math] be the number of children. If one adult eats three rice balls and three children eat one rice ball, which of the following equations systems best describes the situation?

Ashley usually donates some money to her favorite Youtuber. Let [math]f(n)[/math] be a linear function representing the amount of money she donated where [math]n[/math] is the number of weeks after 2024. If Ashley donated $500 in the first week and $460 in the second week, what is the slope of [math]f(n)[/math]?

There is a cup of coffee in a table. Its temperature is [math]52^\circ C[/math]. Two minutes later, its temperature becomes [math]13^\circ C[/math]. If [math]f(t)=a\cdot b^t[/math] represents the temperature of the coffee where [math]a[/math] and [math]b[/math] are constants and [math]t[/math] is measured in minutes, which of the following is true?

In 2023, the price of gasoline is $3.3 per gallon. A truck driver uses an exponential function [math]f(t)[/math] to estimate the price of gasoline per gallon where [math]t[/math] is the number of years after 2023. If the annual growth rate of the price is 4%, what is [math]f(t)[/math]?

The table above shows some values of [math]x[/math] and their corresponding values of the linear function [math]f(x)[/math]. What is the value of [math]a[/math]?

The table above shows some values of [math]x[/math] and their corresponding values of the linear function [math]f(x)[/math]. What is [math]f(4)[/math]?

The table above shows some values of [math]x[/math] and their corresponding values of the linear function [math]f(x)[/math]. What is the slope of [math]f(x)[/math]?

The table above shows some values of [math]x[/math] and their corresponding values of [math]f(x)[/math]. If [math]f(m)=7[/math]. What is the value of [math]m[/math]?

The table above shows some values of [math]x[/math] and their corresponding values of [math]f(x)[/math]. If [math]g(x)=f(x)-2[/math], which of the following tables best represents [math]g(x)[/math]?

The table above shows some values of [math]x[/math] and their corresponding values of [math]f(x)[/math]. Which of the following types of functions cannot be [math]f(x)[/math]?

Let [math]f(x)=6-8x[/math] and [math]g(x)=22[/math]. What is the [math]x[/math]-coordinate of the intersection of [math]f(x)[/math] and [math]g(x)[/math]?

Let [math]f(x)=x^2+7[/math] be a function. If [math]f(m)=13[/math], what is the value of [math]m[/math]?

What is the [math]x[/math]-intercept of the function [math]f(x)=(x+1)^2[/math]?

$$f(x)=7-3(2-x)$$If [math]f(m)=13[/math], what is the value of [math]m[/math]?

The figure above shows the graph of [math]f(x)[/math]. If [math]f(n)=4[/math], which of the following numbers could be [math]n[/math]?

The figure above shows the graph of [math]f(x)[/math]. Which of the following graphs is [math]g(x)+2[/math]?

The figure above shows the graph of [math]f(x)[/math]. Which of the following values is greater than 1?

$$f(x)=\frac{x}{x-2}$$Which of the following functions whose domain is the same as [math]f(x)[/math]?

The figure above shows the graph of [math]f(x)[/math]. What is the range of [math]f(x)[/math]?

$$f(x)=\sqrt{18-x^2}$$If [math]f(a)[/math] is undefined, which of the following values could be [math]a[/math]?

What is the range of the function [math]f(x)=1-|x-1|[/math]?

The table above shows some values of functions [math]f(x)[/math] and [math]g(x)[/math]. What is the value of [math]g(f(4))[/math]?

$$f(x)=(2x+1)^2$$What is the [math]y[/math]-intercept of [math]g(x)=f(f(x))[/math]?

$${}^\circ C=\frac{5}{9}({}^\circ F-32)$$The formula above is used to convert temperature from [math]{}^\circ C[/math] to[math]{}^\circ F[/math]. The temperature of a cup of milk tea was [math]65^\circ C[/math]. A few moments later, its temperature decreased by [math]12^\circ F[/math]. What would the equivalent decrease be in [math]{}^\circ C[/math]?

$$G=aS+13$$The linear equation above represents the relationship between the price of gold [math]G[/math] (USD) and the price of silver [math]S[/math] (USD) where [math]a[/math] is a negative constant. If the price of silver increases by $3 this year, how many dollars of gold decreased this year?

Franky wants to sell his car to buy a new one. He sets a linear function
$$P=-1400T+25000$$To represent the relationship between price [math]P[/math] (USD) and age of car [math]T[/math] (year). Which of the following statements is incorrect?

If [math]2[/math] and [math]-5[/math] are the [math]x[/math]-intercept and [math]y[/math]-intercept of line [math]\ell[/math] respectively, what is the equation of [math]\ell[/math]?

$$\frac{x}{5}-\frac{y}{7}=1$$ What is the [math]y[/math]-intercept of the equation above?

Let [math]f(x)[/math] be a linear function with a slope of [math]\dfrac{1}{3}[/math] and a [math]y[/math]-intercept of [math]-2[/math]. Which of the following points is not on the graph of [math]f(x)[/math]?

$$\ell: 3y=5x-7$$The equation of line [math]\ell[/math] is shown above, what is the slope of [math]\ell[/math]?

$$\ell: ax+by=c$$The equation of line [math]\ell[/math] is shown above. If the [math]x[/math]-intercept of [math]\ell[/math] is 0, which of the following must be true?

If two lines [math]\ell_1: y=2x-b[/math] and [math]\ell_2: y=ax+18[/math] has no intersections, which of the following values is impossible?

Line [math]\ell_1[/math] is perpendicular to line [math]\ell_2[/math]. If the equation of [math]\ell_1[/math] is [math]y=2024x[/math], which of the following equations could be [math]\ell_2[/math]?

If a line is perpendicular to the [math]x[/math]-axis, what is the slope of the line?

Let [math]A(-2,7)[/math] and [math]B[/math] be two points on the [math]xy[/math]-plane. If [math]\overline{OA}[/math] is perpendicular to [math]\overline{OB}[/math] where [math]O[/math] is the origin. Which of the following coordinates could not be [math]B[/math]?

$$\ell_1: y=mx+b$$$$\ell_2: y=-mx+c$$If [math]m\neq1[/math], which of the following statements about two lines [math]\ell_1[/math] and [math]\ell_2[/math] must be true?

$$y<2x+11$$$$y\geq-x+11$$Which of the following is a solution to the inequalities system above?

$$9x+7y=b$$$$ax-21y=-48$$In the given system of equations above, [math]a[/math] and [math]b[/math] are constants. If the system has no solutions, which of the following values could not be [math]b[/math]?

A person spent $2,000 on stock that he believed would rise in value. The next day, he woke up to find the stock’s value had increased to 10% of its original value. If the price of the stock growths exponentially each day, which of the following functions can represent the stock’s price?

The weight [math]w(x)[/math], in kilograms, of a certain elephant from birth can be modeled using the function [math]w(x)=139(1.327)^x[/math] where [math]x[/math] is the number of years from birth. Which of the following best interprets the statement “[math]w(12)[/math] is approximately equal to 4144”?

The population of a city can be represented as the function [math]f(t)=1080(1.02)^t[/math] where [math]t[/math] is the number of years after 2020. Which of the following statements about the number 1.02 is true?

A bag of hot peppers prices tend to be 1.4% more expansive than the year before. What type of function best represents the relationship between the price and year?

After buying a bowl of soup from a street vendor, a customer found a rat in the bowl. Consequently, she wants to spread word about the vendor. Let [math]f(t)=5(1.4)^{2t}[/math] represent the relationship between the time [math]t[/math] (in days) and the number of people who heard about the incident. How many people are estimated to hear about the unsanitary conditions of the street vendor on the fifth day?

The exponential function [math]f(t)=120\cdot(5)^{\frac{t}{4}}[/math]represents the population of mosquitos in a garden, where [math]t[/math] represents the number of day after 2007. What is the meaning of the value 5 in the function?