50 PONTIS Score for Question 3: ___ of 5 points) 3. Solve the given inequality and graph the solution on a number line. Show you
r work! -2x + 3 < 5
2 answers:
Answer:
- x > - 1 or x = (-1, + oo)
Step-by-step explanation:
<h3>Given </h3><u>Inequality </u>
- -2x + 3 < 5
- Solve and graph
- -2x + 3 < 5
- -2x < 5 - 3
- -2x < 2
- x > - 1
- x = (-1, + oo)
As per above, the graph covers all numbers to the right from the point -1
<em>The graph is attached</em>
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Answer: Check out the attached diagram below for the filled out table.
Explanation:
- A) This is correct. You basically stick a minus sign out front to reflect over the x axis (aka the line y = 0).
- B) Replacing x with x+2 will shift the graph 2 units to the left. Adding on 3 at the end will shift it up 3 units.
- C) A vertical stretch, aka vertical dilation, makes the graph taller than it already is. In this case, we want to stretch it to make it twice as tall. That explains the 2 out front. The negative is there to reflect over the x axis.
- D) The -2 is to apply a dilation of 2 and do a reflection. The +6 is so ensure that the vertex arrives at the proper location (0,6) so that we reflect over y = 3.
- E) This is similar to part B. Replacing x with x-3 shifts the graph 3 units to the right. We subtract off 2 at the end to shift the graph down 2 units. The 1/2 out front applies the dilation, which in this case is a vertical compression by a factor of 2.
- F) A vertical compression by a factor of 4 is the same as dilating by a factor of 1/4. So we'll multiply f(x) by 1/4.
- G) Similar to part F, but we'll be using the scale factor 4 this time.
