For the linear function f, the table below displays selected values of x and their corresp… — SAT

For the linear function $f$ , the table below displays selected values of $x$ and their corresponding function values $f(x)$ .

What is the value of $f(10)$ ?

Cevap: 25

The value of

f(10)

is 25.

The correct answer is 25. By using the points

(-2, 1)

and

(2, 9)

, the slope of the linear function is calculated as

m = \frac{9 - 1}{2 - (-2)} = 2

. Substituting this slope and the point

(2, 9)

into the slope-intercept form,

f(x) = 2x + b

, gives

9 = 2(2) + b

, which resolves to

b = 5

. Thus, the linear function is defined by

f(x) = 2x + 5

. Evaluating the function at

x = 10

yields

f(10) = 2(10) + 5 = 25

Calculate the slope of the linear function using two coordinate pairs.

Slope

m = 2

The slope of a linear function can be determined by the formula

m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}

. Substituting

(-2, 1)

and

(2, 9)

yields

m = \frac{9 - 1}{2 - (-2)} = \frac{8}{4} = 2

Find the y-intercept of the function to write its equation.

f(x) = 2x + 5

Substituting the slope

m = 2

and the point

(2, 9)

into the slope-intercept form

f(x) = mx + b

gives

9 = 2(2) + b

, which simplifies to

b = 5

Evaluate the function for the input value 10.

f(10) = 25

Substituting

x = 10

into the linear function equation

f(x) = 2x + 5

yields

f(10) = 2(10) + 5 = 25

Determining a linear function from a table of values and using it to find specific outputs.

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