PSAT: Algebra - Linear Functions

The function $f$ is defined by $f(x) = 25x + 30$. What is the value of $f(x)$ when $x = 2$?

One gallon of paint will cover 220 square feet of a surface. A room has a total wall area of $w$ square feet. Which equation represents the total amount of paint $P$, in gallons, needed to paint the walls of the room twice?

The function $g$ is defined as $g(x) = 5x + a$, where $a$ is a constant. If $g(4) = 31$, what is the value of $a$?

The function $f$ is defined by $f(x) = 4x$. For what value of $x$ does $f(x) = 8$?

The function $f$ defined by $f(t) = 14t + 9$ gives the estimated length, in inches, of a vine plant $t$ months after Tavon purchased it. Which of the following is the best interpretation of 9 in this context?

The table shows four values of $x$ and their corresponding values of $f(x)$. There is a linear relationship between $x$ and $f(x)$ that is defined by the equation $f(x) = mx - 28$, where $m$ is a constant. What is the value of $m$?

$g(m) = -0.05m + 12.1$

The given function $g$ models the number of gallons of gasoline that remains from a full gas tank in a car after driving $m$ miles. According to the model, about how many gallons of gasoline are used to drive each mile?

The cost of renting a backhoe for up to 10 days is $270 for the first day and $135 for each additional day. Which of the following equations gives the cost $y$, in dollars, of renting the backhoe for $x$ days, where $x$ is a positive integer and $x \le 10$?

In the linear function $h$, $h(28) = 15$ and $h(26) = 22$. Which equation defines $h$?

The number $y$ is 84 less than the number $x$. Which equation represents the relationship between $x$ and $y$?

A contract for a certain service requires a onetime activation cost of $35 and a monthly cost of $23. Which equation represents this situation, where $c$ is the total cost, in dollars, of this service contract for $t$ months?

The total cost $f(x)$, in dollars, to lease a car for 36 months from a particular car dealership is given by $f(x) = 36x + 1,000$, where $x$ is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is $\$400$?

Gabriella deposits $35 in a savings account at the end of each week. At the beginning of the 1st week of a year there was $600 in that savings account. How much money, in dollars, will be in the account at the end of the 4th week of that year?

$f(x) = 39$

For the given linear function $f$, which table gives three values of $x$ and their corresponding values of $f(x)$?

The linear function $g$ is defined by $g(x) = b - 15x$, where $b$ is a constant. If $g(c + 7) = \dfrac{c}{4}$, where $c$ is a constant, which of the following expressions represents the value of $b$?

The function $f$ is defined by $f(x) = 8x$. For what value of $x$ does $f(x) = 72$?

The function $f$ is defined by $f(x) = 80 - 6x$. What is the value of $f(7)$?

The function $f$ is defined by $f(x) = 3x - 8$. What is the value of $f(7)$?

The function $f(x)$ is defined as 19 more than 4 times a number $x$. If $y = f(x)$ is graphed in the $xy$-plane, what is the best interpretation of the $x$-intercept?

The graph of the function $f$ is a line in the $xy$-plane. If the line has slope $\dfrac{3}{4}$ and $f(0) = 3$, which of the following defines $f$?

Scientists collected fallen acorns that each housed a colony of the ant species P. ohioensis and analyzed each colony’s structure. For any of these colonies, if the colony has $x$ worker ants, the equation $y = 0.67x + 2.6$, where $20 \le x \le 110$, gives the predicted number of larvae, $y$, in the colony. If one of these colonies has 58 worker ants, which of the following is closest to the predicted number of larvae in the colony?

The function $f$ is defined by $f(x) = 7x - 84$. What is the x-intercept of the graph of $y = f(x)$ in the xy-plane?

In the $xy$-plane, the graph of the linear function $f$ contains the points $(0, 2)$ and $(8, 34)$. Which equation defines $f$, where $y = f(x)$?

An object hangs from a spring. The formula $\ell = 30 + 2w$ relates the length $\ell$, in centimeters, of the spring to the weight $w$, in newtons, of the object. Which of the following describes the meaning of the 2 in this context?

$d = 16t$

The given equation represents the distance $d$, in inches, where $t$ represents the number of seconds since an object started moving. Which of the following is the best interpretation of $16$ in this context?

According to a model, the head width, in millimeters, of a worker bumblebee can be estimated by adding $0.6$ to four times the body weight of the bee, in grams.

According to the model, what would be the head width, in millimeters, of a worker bumblebee that has a body weight of $0.5$ grams?

$f(x) = 8x + 4$

The function $f$ gives the estimated height, in feet, of a willow tree $x$ years after its height was first measured. Which statement is the best interpretation of $4$ in this context?

Marisol drove 3 hours from City A to City B. The equation below estimates the distance $d$, in miles, Marisol traveled after driving for $t$ hours.

$d = 45t$

Which of the following does 45 represent in the equation?

According to data provided by the US Department of Energy, the average price per gallon of regular gasoline in the United States from September 1, 2014, to December 1, 2014, is modeled by the function $F$ defined below, where $F(x)$ is the average price per gallon $x$ months after September 1.

$F(x) = 2.74 - 0.19(x - 3)$

The constant 2.74 in this function estimates which of the following?

For the linear function $f$, $f(0) = 17$ and $f(1) = 17$. Which equation defines $f$?

The equation $h = \dfrac{9(v - 273.15)}{5} + 32$ gives the corresponding temperature $h$, in degrees Fahrenheit, of any substance that has a temperature of $v$ kelvins, where $v > 0$. If a substance has a temperature of 467.33 degrees Fahrenheit, what is the corresponding temperature, in kelvins, of this substance?

The function $f$ is defined by $f(x) = \frac{1}{10}x - 2$. What is the y-intercept of the graph of $y = f(x)$ in the xy-plane?

$j(x) = mx + 144$

For the linear function $j$, $m$ is a constant and $j(12) = 18$. What is the value of $j(10)$?

$f(x) = \frac{x + 7}{4}$

For the function $f$ defined above, what is the value of $f(9) - f(1)$?

The function $f$ is defined by $f(x) = \frac{1}{2}(x + 6)$. What is the value of $f(4)$?

A model predicts that a certain animal weighed 241 pounds when it was born and that the animal gained 3 pounds per day in its first year of life. This model is defined by an equation in the form $f(x) = a + bx$, where $f(x)$ is the predicted weight, in pounds, of the animal $x$ days after it was born, and $a$ and $b$ are constants. What is the value of $a$?

The function $f$ is defined by the equation $f(x) = 100x + 2$. What is the value of $f(x)$ when $x = 9$?

The function $f$ is defined by $f(x) = 4x + k(x - 1)$, where $k$ is a constant, and $f(5) = 32$. What is the value of $f(10)$?

The function $f$ is defined by $f(x) = mx + b$, where $m$ and $b$ are constants. If $f(0) = 18$ and $f(1) = 20$, what is the value of $m$?

Which of the following is the graph of the equation $y = 2x - 5$ in the xy-plane?

The relationship between two variables, $x$ and $y$, is linear. For every increase in the value of $x$ by 1, the value of $y$ increases by 8. When the value of $x$ is 2, the value of $y$ is 18. Which equation represents this relationship?

Some values of the linear function $f$ are shown in the table above. Which of the following defines $f$?

In the $xy$-plane, the graph of the linear function $f$ contains the points $(0,3)$ and $(7,31)$. Which equation defines $f$, where $y = f(x)$?

$f(x) = x + b$

For the linear function $f$, $b$ is a constant. When $x = 0$, $f(x) = 30$. What is the value of $b$?

The function $f$ is defined by $f(x) = -3x + 60$. What is the value of $f(x)$ when $x = -8$?