SAT Questions? HELP!?

Question

The figure above shows the graph of y=g(x). If the function h is defined by h(x)=g(2x)+2, what is the value of h(1)?

in the xy-coordinate plane, the graph of x=y^2-4 interesects line L at (0,p) and (5,t). what is the greatest possible value of the slope of L?

esther drove to work in the morning at an average speed of 45 miles per hour. she returned home in the evening along the same route and averaged 30 miles per hour. if esther spent a total of one hour commuting to and from work, how many miles did esther drive to work in the morning?

Please explain. Thank you!

Answer 1

I can't answer the first one without a picture...sorry.

For the second one, plug in what you know (the x variables from the points):

0=y^2-4

5=y^2-4

Solve for y:

4=y^2

y = +2 or -2

9=y^2

y = +3 or -3

The points to check are:

(0, 2) and (0, -2) versus (5, 3) and (5, -3)

Plot the four points to get an idea of which will have the greatest value.

Plug them in to the slope formula:

m = (y2 - y1)/(x2 - x1)

m = (3 - -2)/(5 - 0)

m = 5/5

m = 1

The other combinations are smaller or negative.

All rate equations have the general form:

distance = rate x time

In this problem, there are two:

the morning speed:

d1 = 45t1

the evening speed:

d2 = 30t2

The two times together must equal one hour:

t1 + t2 = 1

Solve for one of them:

t2 = 1 - t1

The distances are equal (same distance from work as to work). Set them equal to each other, and substitute for t2:

45t1 = 30(1 - t1)

Solve for t1:

45t1 = 30 - 30t1)

75t1 = 30

t1 = 30/75 hours or

t1 = 2/5 hours or

t1 = 24 minutes

Plug in to the first equation:

d1 = (45)(2/5)

d1 = 18 miles

Hope that helps some.