MIDTERM 1

(Section 3.1) find the vertex of the parabola by applying the vertex formula. function: -1/3a^2+ 6a+1

(9,28)

(Section 2.8) Find f(g(x)) FOG and write the domain in interval notation: f(x)=3/x^2-16 g(x)=sqrt(2-x)

(f fog g)(x)=-3/x+14 domain (-infinity,-14) U (-14,2]

(Section 2.8) refer to functions s, t, and v. Find the indicated function and write the domain in interval notation. s(x)=x-2/x^2-9 s(t)=x-3/2-x Function: ( s*t)x

-1/x+3 domain: (-infinity, -3) U (-3,2) U (2,3) U (3, infinity)

(Section 2.8) find the difference quotient and simplify: -5x^2-4x+2

-10x-5h-4

(Section 3.1) a) Write the function in vertex form. B) Identify the vertex. C) Determine the x-intercept(s). D) Determine the y-intercept. E) Sketch the function. F) Determine the axis of symmetry. G) Determine the minimum or maximum value of the function. H Write the domain and range in interval notation. Function: p(x) = 3x^2 − 12x − 7

A)p(x)=3(x-2)^2-19 B) (2,-19) C) (6+ sqrt(57)/3, 0) and (6-sqrt(57)/3,0) D) (0,-7) E) Graph F) x=2 G) min = -19 H) domain: (-infinity, infinity) Range: [-19,infinity)

(Section 2.6) Be able to graph this function: y = 2f(x − 2) − 3.

Graph it

(Section 2.6) Be able to graph this function: f(x)= - | 1/2x-3 |

Graph it

(Section 2.7) Determine if a function is even, odd, or neither: f(x)= sqrt(16-(x-3)^2)

Neither

(Section 2.3) Determine if a relation defines y as a function of x: (x + 1)^2 + (y + 5)^2 = 25

No.

(Section 3.2) determine the end behavior of the graph of the function m(x) = −4(x − 2)(2x + 1)^2(x + 6)^4

Up left down right. As x goes to -finfinity, f(x) goes to infinity. Asx goes to infinity, f(x) goes to -infinity

(Section 2.4) Determine average rate of change for the given interval m(x)= sqrt(x) a) [0,1] b) [1,4] c) [4,9]

a) 1 b) 1/3 c) 1/5

(Section 2.7) a) Find the locations and values of the relative maxima and relative minima of the function on the standard viewing window. Round to 3 decimal places. b) Use interval notation to write the intervals over which f is increasing or decreasing. FUNCTION: 0.4x^2-3x-2.2

a) Rel. min of -7.825 at x= 3.750 b) Increasing on (3.750, infinity); Decreasing on (-infinity, 3.750)

(Section 2.3) Determine domain and range from it's function: a) f(x)= sqrt(x+15) b) f(x)= sqrt(x+15) -2 c) f(x)= 5/sqrt(x+15) -2

a) [-15, infinity) b) [-15, infinity) c) [-15,-11) U (-11,infinity)

(Section 2.7) a) Graph the function: -x^2+1 for x<=1 2x for x > 1 b) Write the domain in interval notation. c) Write the range in interval notation. d) Evaluate f(−1), f(1), and f(2). e) Find the value(s) of x for which f(x) = 6. f) Find the value(s) of x for which f(x) = −3. g) Use interval notation to write the intervals over which f is increasing, decreasing, or constant.

a) graph b) (-infinity, infinity) c) (-infinity, 1] U (2, infinity) d) f(-1)=0, f(1)=0, and f(2)=4 e) x=3 f) x=-2 g) Increasing: (-infinity, 0) U (1,infinity) decreasing (0,1) Never constant

(Section 2.3) Evaluate the function: f(x)=(x^2+3x) f(a + 4)

a^2+11a+28

(Section 2.7) a) Graph p(x) = x + 2 for x ≤ 0. b) Graph q(x) = −x^2 for x > 0. c) Graph r(x)= x+2 for x<=0 -x^2 for x>0

graph

(Section 2.8) find two functions f and g such that h(x)=(f fog g(x))

h(x)=| 2x^2-3| f(x)= |x| g(x)=2x^2-3

(Section 2.7) determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, origin, or none of these: x = −|y| − 4

symmetric to x axis

(Section 2.8) find (f fog f(x)) and write the domain in interval notation. Function: 1/x-2

x-2/-2x+5 Domain: (-infinity,2) U (2,5/2) U (5/2, infinity)

(Section 2.6) Write a function based on the given parent function and directions: Parent function: y=x^3 1) Shift 4.5 units to the left 2) Reflect across the y axis

y=(-x+4.5)^3+2.1