i put 4 graphs in my answer
Slope intercept form: y = mx + b --- m is slope and b is y-int
f(x) = x has a slope of 1 and y-intercept of 0
So you can graph a dot at (0,0). Since slope = 1 and slope is rise/run, from (0,0) rise up 1 unit and run right 1 unit to go to (1,1). Put a dot there then draw a line
g(x) = (x + 2) -3 we can rewrite as g(x) = x+2-3 = x - 1
y-intercept at 1.
Graph a dot at (0,-1). Slope is still 1, so rise up 1 and run right 1 to go to (1,0). Plot and draw line
for 2(h(x)); h(x) = x-1, we want to graph 2(h(x)).
since h(x) = x-1, 2( h(x) ) = 2(x-1) = 2x - 2
slope of 2, y intercept of -2
see graph
d(x) = 1/2x +2
slope of 1/2 and y-intercept at 2
start at (0,2). rise 1 and then run 2 units to go to (2,3)
the transformations in words
f(x) —›g(x)
g(x) is the graph of f(x) translated 2 units left and translated 3 units down.
f(x) —›h(x)
h(x) is the graph of f(x) vertically expanded by a factor of 2 and then translated 1 unit right.
f(x) —›d(x)
d(x) is the graph of f(x) horizontally expanded by a factor of 2 and then translated 2 units up.
