The graph of the parent function f(x)=x^3 is transformed such that g(x)=f(-2x). how does the graph of g(x) compare to the graph of f(x)?

look down

Step-by-step explanation:

1:

   Dividing the function by 2 divides all the y-values by 2 as well. So to get the new point, we will take the y-value (4) and divide it by 2 to get 2.

   Therefore, the new point is (−12,2)

2:

   Subtracting 2 from the input of the function makes all of the x-values increase by 2 (in order to compensate for the subtraction). We will need to add 2 to the x-value (−12) to get −10.

   Therefore, the new point is (−10,4)

3:

   Making the input of the function negative will multiply every x-value by −1. To get the new point, we will take the x-value (−12) and multiply it by −1 to get 12.

   Therefore, the new point is (12,4)

4:

   Multiplying the input of the function by 4 makes all of the x-values be divided by 4 (in order to compensate for the multiplication). We will need to divide the x-value (−12) by 4 to get −3.

   Therefore, the new point is (−3,4)

5:

   Multiplying the whole function by 4 increases all y-values by a factor of 4, so the new y-value will be 4 times the original value (4), or 16.

   Therefore, the new point is (−12,16)

6:

   Multiplying the whole function by −1 also multiplies every y-value by −1, so the new y-value will be −1 times the original value (4), or −4.

   Therefore, the new point is (−12,−4)

Final Answer

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

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step-by-step explanation: