Question

Graph. f(x)=|2x+4|+1

Answer 1

Answer:

Step-by-step explanation:

Best if we begin with the basic graph of the absolute value function.  It looks like a "V" that opens up and has its vertex (sharp point) at the origin, (0, 0).The equation looks like f(x) = |x|. Next, consider what would happen if you were to move the entire graph 1 unit to the right.  The equation would become f(x) = |x-1|.  Note the - sign.  If you move the vertex back to the origin and then move the entire graph 5 units to the left, the equation would be f(x) = |x+5|.  Note the + sign here.Consider what would happen if you were to start with the basic graph of f(x) = |x| and move the entire graph d units upward.  The equation would then be f(x) = |x| + d.Now let's look at your f(x)=|2x+4|+1.  We'll factor out the 2 in |2x+4|, obtaining 2|x+2|.  See that + sign?  The vertex of |x+2| will be 2 units to the LEFT of the origin, (0, 0).  Draw this.  Next, noticing the +1 in your f(x)=|2x+4|+1, we move the entire graph up 1 unit.

Note that in this graph, the right hand half looks like the graph of y = x, with a slope of 1.  This part of the graph makes a 45 degree angle with the x-axis.  But your f(x)=|2x+4|+1, now in the form f(x) = 2|x+2|+1, has the multiplier 2 in front of |x+2|.  The effect this has on the graph is to STRETCH IT vertically.  The right half of your graph now has the slope 2, instead of 1, and the left half has the slope -2 instead of -1.  

Answer 2

Answer:

Step-by-step explanation:

Best if we begin with the basic graph of the absolute value function.  It looks like a "V" that opens up and has its vertex (sharp point) at the origin, (0, 0).

The equation looks like f(x) = |x|.

I'd suggest you draw this right now.

Next, consider what would happen if you were to move the entire graph 1 unit to the right.  The equation would become f(x) = |x-1|.  Note the - sign.  If you move the vertex back to the origin and then move the entire graph 5 units to the left, the equation would be f(x) = |x+5|.  Note the + sign here.

Consider what would happen if you were to start with the basic graph of f(x) = |x| and move the entire graph d units upward.  The equation would then be f(x) = |x| + d.

Now let's look at your f(x)=|2x+4|+1.  We'll factor out the 2 in |2x+4|, obtaining 2|x+2|.  See that + sign?  The vertex of |x+2| will be 2 units to the LEFT of the origin, (0, 0).  Draw this.  Next, noticing the +1 in your f(x)=|2x+4|+1, we move the entire graph up 1 unit.

Note that in this graph, the right hand half looks like the graph of y = x, with a slope of 1.  This part of the graph makes a 45 degree angle with the x-axis.  But your f(x)=|2x+4|+1, now in the form f(x) = 2|x+2|+1, has the multiplier 2 in front of |x+2|.  The effect this has on the graph is to STRETCH IT vertically.  The right half of your graph now has the slope 2, instead of 1, and the left half has the slope -2 instead of -1.  

This completes the graph.