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