1.2.1 Functions

Question 1

Functions

Answer 1

• A function pairs one object with another. A function will produce only one object for any pairing.
• A function can be represented by an equation. To evaluate the function for a particular value, substitute that value into the equation and solve.
• You can evaluate a function for an expression as well as for a number. Substitute the entire expression into the equation of the function. Be careful to include parentheses where needed

Question 2

note

Answer 2

• A function is a mathematical machine that takes one value and produces another one. In the example of an ATM machine, each account number matches up to exactly one balance.
• Here the function machine is called f. f takes a value x and returns another value f(x).
• This notation is an improvement over y-notation. It allows you to write f(5) to mean “the value of the function when x equals 5.”
• The symbol f(5) is read as “f of 5.”
• If you have a function whose inputs are numbers, then you can also use variables to represent those numbers.
• For example, f(a) produces the value of the function f when the value of a is used as the input.
• You can even evaluate a function for a number that is
  represented by an expression such as a + b. In this example, make sure to replace every appearance of x with the expression a + b. If x is squared, you must square the entire expression. If x is multiplied by 2, you must multiply the entire expression by 2. Use parentheses to help you keep track.
• The most common name for a function is f, but sometimes it makes sense to name a function g, p, v, or even something else.

Question 3

The amount of money in Brian’s savings account is given by the function M (t) = 50t^ 2 + 100t + 80, where t is the time in years. Approximately how many years will it take Brian to save $1,000?

Answer 3

None of the above

Question 4

A function is defined as f (x) = x 2 − 5x + 3. Evaluate f (1).

Answer 4

f (1) = −1

Question 5

A function is defined as f (x) = −2x + $6. Evaluate f ($2.20).

Answer 5

f ($2.20) = $1.60

Question 6

A function is defined as

f (x) = 3x^ 3 − 4. Evaluate f (2).

Answer 6

f (2) = 20

Question 7

Given the graph of f (x), find the best estimate of f (3).

Answer 7

−2

Question 8

Given the graph of f (x), find the best estimate of f (2).

Answer 8

f (2) = 1

Question 9

If f (x) = 3x ^2 − 10, which of the following is the new function defined by g (x) = f (x − 1)?

Answer 9

g (x) = 3x ^2 − 6x − 7

Question 10

If h (t) = 50t ^5 + 50t ^3 + 50t, what is h (COW)?

Answer 10

h (COW) = 50 (COW^)5 + 50 (COW)^3 + 50 (COW)

Question 11

If g (x) = −2x + 7, which of the following is the new function defined by h (x) = g (2x ^2 + 1)?

Answer 11

h (x) = −4x^ 2 + 5

Question 12

Suppose the function 
g(x) = 4x^3 - 3x - (2x-1)/5x+4
find g(-4)

Answer 12

g(-4) = -244 and 9/16

Question 13

Given that T ( y) = y^2 − 3y + 5, compute T (x + Δ x).

Answer 13

T (x + Δ x) = x^ 2 + 2 xΔ x + (Δx)^ 2 − 3x − 3Δ x + 5

Question 14

Rob’s height from birth to 15 years is modeled by the function h (t) = 0.24t^  2 + 22, where t is his age in years, and h (t) is his height in inches. At what age is Rob 76 inches tall?

Answer 14

15 years

Question 15

Given the graph of g (x), find the best estimate of g (4)

Answer 15

1

Question 16

Maria’s height from birth to 12 years is modeled by the function h (t) = 0.26t^ 2 + 22, where t is her age in years, and h (t) is her height in inches. What is Maria’s height when she is 10 years old?

Answer 16

None of the above