math 4 unit 1/midterm review
the function f(x) is hrizontally stretched by a factor of 6, shifter to the right 2, vertically compressed by a factor of .5 and shifted up 7. write the new equation for f(x).
.5(1/6x-2)^2 +7
a cos + b what do a and b represent?
a= amplitude b= height
y = ab^x , b>1 model type? domain? range?
exponential (-∞,∞) (0,∞)
f(x)=sin x vertically stretched by a factor of 2 and shifted down 3 rule? period? amplitude?
g(x)= 2sin(x)-3 2pi 2
f(x)=sin x horizontally stretched by a factor of 6 and vertically stretched by a factor of 3 rule? period? amplitude?
g(x)=3sin (1/6x) 12pi 3
inside parenthesis
horizontal scale factor is opposite (ex. 3=1/3) subtraction=right, addition= left
describe how f(3x) relates to f(x)
horizontally compressed, sf of 1/3
y = 1/x^2 model type? domain? range?
inverse (-∞,0) u (0,∞) (0,∞)
y = a + bx model type? domain? range?
linear (-∞,∞) (-∞,∞)
how do you find the zeroes?
numerator equal to zero when in factored form
what information about the graph of the function is easily obtained by looking at expression III but not by looking at the other forms?
oblique asymptotes
how do you find the y int?
plug zero into equation
y = ax^5 , a>0 model type? domain? range?
power (-∞,∞) (-∞,∞)
describe how -4f(x) relates to f(x)
reflects over x-axis, vertically stretched by sf 4
how do you find the vertical asymptotes?
set denominator equal to zero
describe how f(x-6)+2 relates to f(x)
shift right 6, shift up 2
describe how f(x)+3 relates to f(x)
shift up 3
y = 5cosx model type? domain? range?
trig (-∞,∞) [-5,5]
outside parenthesis
vertical scale factor is same