Function Operations
f(x) = 5x - 3
g(x)= 2 - x
FIND h(x) = - f(x) + g(x)
h(x) = - 6x + 5
f(x) = 4x - 2
FIND f-1(x)
f-1(x)= 1/4x + 1/2
Determine whether the equation is a linear equation, 9xy-6y=7.
No.
When a function and its inverse intersect, what must be true about the point of intersection?
The intersection point is the solution to BOTH functions.
When graphing less than or equal to, what kind of boundary line is used?
SOLID line
f(x) = 5x - 3
g(x)= 2 - x
FIND j(x) = -2f(x) - g(x)
j(x)= -9x + 4
g(x) = (x+5)/7
FIND g-1(x)
g-1(x)= 7x - 5
Solve.
0 = 21 - 3x
x= 7
What is the slope of a line that is parallel to another line with the slope of -2/5.
-2/5
Where will the shading for 5x - y > 10 be?
under? above? AND right? left?
UNDER the boundary line, to the right
f(x) = 5x - 3
g(x)= 2 - x
FIND k(x) = 6g(x) - f(-3)
k(x) = - 6x + 30
h(x)= 1/2x + 2/3
FIND h-1(x)
h-1(x)= 2x - 4/3
f(x) = 5/9 (x - 32) can be used to convert the temperature from Fahrenheit to Celsius. How can you determine the temperature in F when the temperature is given in C?
Bonus point: FIND the temperature in F for -25 degrees Celsius.
Find the inverse function!
f-1(x)= (9/5)x +32
Bonus: - 13 degrees F!
Write an equation of the line that passes through (2,1) with the slope of 3.
y= 3x - 5
5x - y > 10
Be specific, describe the graph/solutions.
dotted line y < 5x - 10, shaded under boundary line, or to the right
f(x) = 5x - 3
g(x)= 2 - x
FIND m(x) = f(-2)*g(-10)
m(x)= - 156
Baxter thinks 2x - 3y >= 6 should be shaded above the boundary line. Do you agree/disagree? Explain
>= is greater than or equal to
DISAGREE. When you divide by a negative number, the inequality sign flips over.
B(t)= the number of boys who attended a school in year t
G(t)= the number of girls who attended the same school in year t
Explain what R(t) = B(t) + G(t) represents.
The TOTAL number of boys and girls who attended the school in year t
Let f(x)=3, g(x)= -2x + 5, h(x)= x - 4
FIND j(x)= f(x)*[g(x)+h(x)]
j(x)= -3x + 3
Describe the graph/solutions.
3x + 2y >= 12
>= means greater than or equal to
y >= (-3/2)x + 6
shaded above, or to the right
f(x) = 5x - 3
g(x)= 2 - x
FIND p(x) = f(x)*g(x)
p(x) = - 5x2 +13x - 6
What are the solutions to:
2x - 3y > 6
Describe y < 2/3x - 2
Find the slope of the line that passes through (0,-4) and (0,2).
Bonus: what is the equation of the line?
undefined
Bonus: x = 0
Let f(x)=3, g(x)= -2x + 5, h(x)= x - 4
FIND k(x) = [f(x)*g(x)] + [f(x)*h(x)]
BONUS:
j(x)= f(x)*[g(x)+h(x)]
FIND r(x)= j(x) - k(x)
k(x)= -3x + 3
BONUS:
r(x)= 0
- x < - 5
Describe the graph/solutions.
vertical dotted line x>5, shading to the right