Domain and Range
What is the domain of the function f(x) = 2x + 1?
All real number
Find the inverse
f(x)= 4/7x + 5
7/4x - 35/4
Determine any non-permissible values:
sec(x)/sin(x)
Find vertical asymptote
f(x)=3x+1/2x-1
x = 1/2
What is the amplitude of y = 2sin (x - pi/4 ) - 2
2
Find the domain of this function f(x) = f(x) = 2x^2 - 3x + 1
All real numbers
y = -3 f(2x - 4) + 1 has what horizontal translation?
Simplify to sinx, cosx, or tanx
(cosx)(cscx)/(secx)(cotx)
cosx(1/sinx)/(1/cosx)(cosx/sinx)
=(cosx/sinx)/(1/sinx)
=(cosx/sinx)(sinx/1)
=cosx
Find horizontal asymptote
f(x)=x+4/x-1
x - 1 + 1 + 4 / x-1
1 + 5/x-1 = 5/x-1 + 1
HA = y = 1
What is the period of Y=2sin6x
Pi/3
Find the domain of function f(x) = 1/x-2
x =/2
f(x) = 3x/5 - 3
f-1(x) = ?
5x/3 + 5
Determine the exact value of this trig expression.
cos(pi/12)
HINT: use sum/difference identity
Example: cos[(pi/3) - (pi/4)]
cos(pi/3)cos(pi/4) + sin(pi/3)sin(pi/4)
(1/2)(sqrt2/2) + (sqrt3/2)(sqrt2/2)
(sqrt2/4) + (sqrt6/4) = (sqrt2 + sqrt6)/4
Find the point of discontinuity
(x2 - 3x - 4) / (x - 4)
x = 4
(plug in x value to solve for y)
hole at (4, 5)
What is the Vertical shift of y = 2cos (x + 3p/4 ) + 1
1 up
Let f(x) = x + 2 and g(x) = x + 3. Determine the equation for h(x) = f(x)/g(x) and state the domain.
(x+2) / (x+3)
D: {x|x=/3, xER}
Write the function with the following transformations:
y = sqrt(x)
vert stretch by factor 3
reflect in x axis
translation 4 units right
translation 2 units down
y = -3 sqrt(x - 4) - 2
Rewrite in terms of sine or cosine, then solve algebraically for 0 <= x < 2pi
cosx + cos2x = 0
cosx + 2cos2x - 1 = 0
2cos2x + cosx - 1 = 0
(2cosx - 1) (cosx + 1) = 0
cosx = 1/2, cosx = -1
x(reference angle) = pi/3 and 0
cos positive in Q1, Q4. Cosx = -1 at pi
x = pi/3, pi, 5pi/3
Find vertical asymptote, horizontal asymptote, and point of discontinuity where possible.
y = (x2 + 3x - 4)/(x2 + 2x - 8)
VA: x = 2
HA: y = 1
Hole: x = -4
What is the period and vertical shift of y = 2sin (x - pi/4 ) - 2
2 pi and 2 down
If f(x) = x - 5 and g(x) = sqrt(x), determine the equation for h(x) = g(f(x)) and state the domain.
g(f(x)) = sqrt(x - 5)
D: {x|x =/5, xER}
Let the original function be y = x5. For the function y = -2 (1/3(x - 1))5 + 4, what is the horizontal stretch factor?
3
Determine the missing coordinate for the point P(x, -2/3) in Q3 on the unit circle.
x2 + y2 = 1
x2 + (-2/3)2 = 1
x = +/- (sqrt5)/3
since x is negative in Q3, x = - sqrt5/3
Write a function with:
point of discontinuity: (3, 2)
VA: x = 1
x-intercept: x = -1
what is the period, amplitude, vertical displacement, and phase shift of y = -5 sin (1/2(x - 90)) + 15
NOTE: In degrees
Period: 360/b = 360/(1/2) = 720 degrees
amplitude: a = 5 (the negative is just a reflection)
vert displacement: up 15
phase shift: right 90 degrees