Evaluating Functions
If f(x) = 3x + 2, find f(4).
f(4) = 3(4) + 2 = 14.
A function has the domain −3 ≤ x ≤ 5. Is x = 6 in the domain?
No. The domain only includes values from −3 through 5.
2x = 4
x = 2
Given f(x) = 4x − 3, a student finds f(2) = 4(2) − 3 = 8 − 3 = 11. What mistake did the student make?
The arithmetic is incorrect. 8 − 3 = 5, so f(2) = 5.
If g(x) = 2x − 7, find g(−3).
g(−3) = 2(−3) − 7 = −13.
A table has these input values: −4, 0, 2, 7. What is the domain?
{−4, 0, 2, 7}.
Solve for x
3 + x = 10
x = 7
Given g(x) = 2x + 5,
a student finds g(−3) = 2(3) + 5 = 11.
What mistake did the student make,
and what is the correct answer?
The student dropped the negative sign when substituting −3.
The correct calculation is g(−3) = 2(−3) + 5 = −1.
If h(x) = 5x − 4, find h(6).
h(6) = 5(6) − 4 = 26.
A graph begins at x = −2 and ends at x = 6. Both endpoints are included. Write the domain using an inequality.
−2 ≤ x ≤ 6.
Solve for X
3x -9 = 15
x = 8
A student answers a test question about rannge and states it is all the x values of a function.
Range is all the y values of a function
or
domain is all the x values of a function
If f(x) = 8 - 3x, find f(−4).
f(-4) = 20
A school sells tickets for $4 each. The school can sell at most 150 tickets. Let x represent the number of tickets sold. Write a reasonable domain. (Think about types of numbers that can be used.)
0 ≤ x ≤ 150, where x is a whole number.
or All Whole Numbers
solve for x
x/6 - 9 = 6
x = 90
A student says the domain of a function with input values −2, 1, 5, and 9 is {−2, 1, 5, 9, 12} because 12 is the largest output. What mistake did the student make?
An output is not part of the domain. The domain is {-2, 1, 5, 9}
If g(x) = x² − 3x + 2, find g(4).
g(4) = 6.
What is the definition of domain? (hint: it is more than just x.)
All the possible inputs of a function.
Solve for x
2x + 4 = 4x - 2
x = 3
For the function f(x) = 2(x+4), evaluate for f(5).
A student shows his work. Where is the mistake?
f(5) = 2(5) + 4
f(5) = 14
The parentesis are in the wrong place or the input should be added to 4, then multiplied by 2
or f(5) = 2(5+4)
f(5) = 18