How do you find the real roots of the following equation?
by cross multiplying
by multiplying the two terms by both denominators
For transformations, what happens when a > 1?
vertical stretch by a
vertical compression by a
For transformations, what happens when k > 1
horizontal compression by 1/k
horizontal stretch by 1/k
For transformations, when (a) is negative there is a reflection of the x axis and when (k) is negative there is a reflection of the y axis.
If d is positive in the general transformed form that means ______________
d is negative and moves the graph to the left
d is positive and moves the graph to the right
How do you find the real roots of this equation?
by multiplying both sides by x (b-x)
by factoring out the gcf
This equation corresponds with
log (b) x = y
log (b) y = x
log (x) b = y
log (y) x = b
Both equations equal
a
log
x
How do you calculate log (a) x?
(log x)/(log a)
(log a)/(log x)
How is this equation calculated?
ln (98)/ ln (12) = x
ln (12)/ ln (98) = x
125^(2x) corresponds with
2 ln 125
125 ln 2
21 ln 25
(5 ln (8))/(3 ln (8) - (6 ln (3)) = x
(3 ln (8))/(6 ln (3)) - (5 ln (8)) = x
(6 ln (3))/(5 ln (8) - (3 ln (8)) = x
How do you calculate this equation?
(5 ln (8)) + (7 ln (3))/(3 ln (8)) - (6 ln (3))
(5 ln (8)) + (3 ln (8))/(7 ln (3))- (6 ln (3))
(5 ln (8)) - (7 ln (3))/(3 ln (8)) + (6 ln (3))
(3^5 - 1) ⚫ 3^x = 177 876 corresponds with the equation in the image
yes.
no, it's (3^5 + 1) ⚫ 3^x = 177 876
if we factor 8^(x+7) - 8^x, you get (8^7 -1) ⚫ 8^x
select every true statement
f(x) =/= f(-x) =/= -f(x) → f(x) is neither
f(x) = f(-x) → f(x) is even
f(-x) = -f(x) →f(x) is odd
f(-x) = -f(x) →f(x) is neither
f(x) =/= f(-x) =/= -f(x) → f(x) is even
f(x) = f(-x) → f(x) is odd
this formula helps find the __________
instantaneous rate of change
the average rate of change
How do you find the instantaneous rate of change?
by using ( f(x + 0.0001) + f (x) ) / 0.0001
by using ( f (x2) - f (x1) ) / (x2) - (x1)
Given that f(x)=x+1 and g(x)= 7x^2+11x−9 what would the equation for g (o) f be?
7(x + 1) ^2+11(x + 1) − 9
(7x^2+11x−9 ) + 1
How do you calculate a DEPRECIATION rate?
new worth = original worth (1-r)^(number of years)
new worth = original worth (1+r)^(number of years)
the formula used to find an APPRECIATION rate is new worth = original worth (1-r)^number of years
If the instantaneous rate of change is positive on the LEFT side of the turning point and negative on the RIGHT side of the turning point, it means that the turning point is a MINIMUM
If the instantaneous rate of change is negative on the left side of the turning point and positive on the right side of the turning point, it means that the turning point is a _________
minimum
maximum
What's the formula for finding an angle in radians?
(arc length) / (radius)
(radius) / (arc length)
(arc length) / (radians)
Functions can only be combined if _____________
they have a common domain
they have a common range
they have a common degree
they have common graph
When combining functions, keep the _ values the same while applying the operations to the _ values
x, y
y, x
x^2+ rx + sx + c where r ◉ s = c and r + s = b
which polynomial am I factoring?
complex trinomial
simple trinomial
complex binomial
complex polynomial
(ax^2+bx+c where r ◉ s = ac and r + s = b) is used to factor a COMPLEX trinomial
How convert an angle in DEGREES to RADIANS? (180 D, 180 DOWN)
angle in degrees x (180/π) = angle in radians
angle in degrees x (π/180) = angle in radians
How to convert an angle in RADIANS to DEGREES? (180 R, 180 RISE)
angle in radians x (180/π) = angle in degrees
angle in radians x (π/180) = angle in degrees
select every true statement concerning sinusoidal functions. read your answers carefully.
d is the starting point.
a is the starting point.
to find a, we use the formula: (maximum + minimum)/ (2)
to find c, we use the formula: (maximum - minimum)/ (2)
to find a, we use the formula: (maximum x minimum)/ (2)
the amplitude is the length of one cycle.
the period is the length of one cycle.
(2pi)/ (period) is the formula used to find k.
(period)/ (2pi) is the formula used to find k.
(2pi) x (period) is the formula used to find k.
when the multiplicity of a factor is even, the graph ______
crosses the x axis
bounces off the axis
when the multiplicity of a factor is odd, the graph ______
bounces off the x axis
when it comes to the equation ( ax + b ) / ( cx + d), select every statement that is true.
we can find its vertical asymptote by finding the x intercept of the denominator
we can find its horizontal asymptote by dividing a/c
we can find its x intercept by solving the numerator
we can find its y intercept by setting x's of the equation to 0
we can find its horizontal asymptote by dividing c/a
we can find its vertical asymptote by finding the y intercept of the numerator
we can find its x intercept by setting y's of the equation to 0
we can find its x intercept by solving the denominator
in trigonometry, which functions are EVEN?
cot
tan
sin
csc
sec
cos
how do you determine the domain and range of this function?
when a is negative: { YER l y < c }
when a is positive: { YER l y > c }
when k is positive: { XER l x > d}
when k is negative: { XER l x < d }
when k is negative: { XER l x > d }
when a is positive: { YER l y < c }
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