SAT Math Lesson 9 - Functions & Graphs! p3_4

13. The figure above shows the graph of y = g(x).
If the function his defined by h(x) = g(2x) + 2. What is the value of h(1)?
Solution:
h(x) = g(2x) + 2
because we need get the value of h(1), so we can substitute 1 for x
h(1) = g(2*1) + 2
h(1) = g(2) + 2 number 2 on g(2) is absis.
 g(2) is ordinate when the absis=2.
 (2 , g(2)) on h(x)= g(2x) +2
We find ordinate when x=2 which (2,y) on h(x)
From the picture we can see y=1
 (2, g(2)) = (2,y)
g(2) = y
g(2) = 1
h(1) = g(2) +2
h(1) = 1 + 2
h(1) = 3
17. In the xy –coordinate plane, the graph of x = y^2 -4 intersects line A at (0,p) and (5,t). What is the greatest possible value of the slope of A?
Solution:
greatest m x = y^2 -4
If we subs x =0 so y = p
If we subs y =t so x = 5
Line A: m=(y2 - y1) / (x2 - x1)
m =(t – p) / (5 – 0)
m =(t – p) / 5