Interpreting Function Notation, Graphs, and Context
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- (Video) Function Notation by PatrickJMT Here's a video by PatrickJMT where he explains function notation. Before, we would express equations in the form: y=x2+xy=8x−5y=x^2+x\\ y…
By Victor Wang, Alex Federspiel, Ruiran Xun, Vatsal Ojha, Caroline K
Problems 29
- Suppose that fff is a linear function and f(4)−f(1)=5f(4)-f(1) = 5f(4)−f(1)=5. Compute f(10)−f(1)f(10)-f(1)f(10)−f(1).
- Suppose that f(2x+3)=x2−x+1f(2x+3) = x^2-x+1f(2x+3)=x2−x+1. Compute f(7)f(7)f(7).
- A function N=f(y)N = f(y)N=f(y) gives the number of police officers, NNN, in a town in year yyy. What does f(2005)=300f(2005) = 300f(2005)=300 tell us?
- The amount of garbage, GGG, produced by a city with population ppp is given by G=f(p)G=f(p)G=f(p). Variable GGG is measured in tons per week, and ppp is measured in thousands of…
- Let f(t)f(t)f(t) be the number of ducks in a lake ttt years after 1990. Explain the meaning of each statement: a.f(5)=30b.f(10)=40\begin{align} &\text{a.}\quad f(5)=30\\ &\text{…
- Let hhh be the height above ground, in feet, of a rocket ttt seconds after launching. Explain the meaning of each statement: a. h(1)=200b. h(2)=350\begin{align}&\text{a. }h(1)=2…
- x0123456789f(x)742815356336451447\begin{array}{|l|l|} \hline x&0&1&2&3&4&5&6&7&8&9\\ \hline f(x)&74&28&1&53&56&3&36&45&14&47 \\ \hline \end{array}xf(x)0741282135345653636…
- x0123456789f(x)628738867370397534\begin{array}{|l|l|} \hline x&0&1&2&3&4&5&6&7&8&9\\ \hline f(x)&62&8&7&38&86&73&70&39&75&34\\ \hline \end{array}xf(x)0621827338486573670…
- Using the graph above, find f(c)f(c)f(c).
- Let f(x)=[x]f(x)=[x]f(x)=[x], where [x][x][x] denotes the greatest integer less than or equal to xxx. Find f(−2.009)f(-2.009)f(−2.009).
- The equation y=x2−5z+3y=x^2-5z+3y=x2−5z+3 expresses yyy as a function of xxx and zzz. What is the dependent variable?
- Consider the following table. Identify the independent and dependent variables in order from top to bottom.
- You are a restaurant trying to determine the price of your salads. Let Ps=Price total of saladP_s=\text{Price total of salad}Ps=Price total of salad, Al=Amount of lettuce order…
- The owner of a new racing team is trying to estimate the cost for each series before he commits to one. He has come up with the following variables: Cost=Total cost of seasonA=A…
- If f(x)=x2+x+1f(x)=x^2+x+1f(x)=x2+x+1, what is f(x−2)f(x-2)f(x−2)?
- If f(x)=3xf(x)=3^xf(x)=3x and g(x)=4xg(x)=4xg(x)=4x, what is f(x−1)+g(y)f(x-1)+g(y)f(x−1)+g(y)?
- Alex has modeled his success with crossword puzzles as the following: n=4s+6hn=4s+6hn=4s+6h Where: n=Number of words filled ins=Hours of sleep the night beforeh=Number of people…
- In Macroeconomics, Gross Domestic Product (GDP) is defined as GDP=C+I+G+NX\text{GDP}=C+I+G+NXGDP=C+I+G+NX Where C=ConsumptionI=InvestmentG=Government spendingNX=Net Exports\begi…
- The number of cards left in a standard deck of cards while playing a game can be modeled as: C=52−P⋅S−DC=52-P\cdot S-DC=52−P⋅S−D Where: C= Cards left in deckP= Number of players…
- Let ttt be the time elapsed since you've thrown a large soda at your neighbor in seconds (who happens to be your mortal enemy) and ddd be the distance between the cup of soda an…
- You just got home from college and your dog is running towards you. The speed of your dog in meters per second(m/sm/sm/s) can be modeled as: S=2w+8S=2w+8S=2w+8 Where: S= Speed o…
- What is f(x)+g(x−2)f(x)+g(x-2)f(x)+g(x−2), given: f(x)=12x−2g(x)=3x2\begin{align} f(x)&=12x-2\\ g(x)&=3x^{2} \end{align}f(x)g(x)=12x−2=3x2
- Vending machines are an example of how functions can be used in real life. A vending machine equation is modeled by the equation P=M+BP=M+BP=M+B Where P=product received from ma…
- Let ggg be a student's grade percentage in a class after ttt hours of sleep on average per night. Explain the meaning of each of the following statements: g(8)=0.98g(4)=0.51\beg…
- Based on the table below, what is f(x)f(x)f(x)? x12345f(x)4681012\begin{array}{|l|l|} \hline x&1&2&3&4&5\\ \hline f(x)&4&6&8&10&12\\ \hline \end{array}xf(x)142638410512
- Nicholas decided today to start calculating how much pollution was in the air. P(t)P(t)P(t) denotes the amount of pollution PPP (measured in parts per million) in the air at tim…
- Based on the table below, what is f(x)f(x)f(x)? x−2−1012f(x)63236\begin{array}{|l|l|} \hline x&-2&-1&0&1&2\\ \hline f(x)&6&3&2&3&6\\ \hline \end{array}xf(x)−26−13021326
- x−2−1012f(x)647786\begin{array}{|l|l|} \hline x&-2&-1&0&1&2\\ \hline f(x)&6&47&7&8&6\\ \hline \end{array}xf(x)−26−147071826 Based on the table above, what are all the xxx…
- What are the independent and dependent variables of the following equation? y=x4−x+2y=x^{4}-x+2y=x4−x+2