Use what you know about horizontal and vertical shifts of functions to sketch a graph of y=log(x-2)+5
1 answer:
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Answer:
A: -1, 3/5
B: (-1/5, -3 1/5)
2: plot the given points and draw a curve through them.
Step-by-step explanation:
<h3>Part A</h3>The x-intercepts are most easily found from a graph of the function. I like the Desmos graphing calculator for this purpose. The x-intercepts are -1 and 3/5.
You can also find the x-intercepts by factoring the function.
f(x) = 5x^2 +5x -3x -3 = 5x(x +1) -3(x +1) = (5x -3)(x +1)
The x-intercepts are the values of x that make the factors zero:
5x -3 = 0 ⇒ x = 3/5
x +1 = 0 ⇒ x = -1
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<h3>Part B</h3>The vertex is on the axis of symmetry, which is the vertical line at the value of x halfway between the zeros. (-1 +3/5)/2 = (-2/5)/2 = -1/5
The value of f(x) there is ...
f(-1/5) = (5(-1/5) +2)(-1/5) -3 = (-1 +2)(-1/5) -3 = -1/5 -3 = -3 1/5
The vertex is (-1/5, -3 1/5).
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<h3>Part 2</h3>The easiest step to take to graph the function is to type it into a graphing calculator (see attached).
If you're graphing this by hand, the three points given in parts A and B will be on the graph. The leading coefficient in the function is 3, so the x^2 parent function is vertically stretched by a factor of 3. This can make it a little more difficult to find points that lie on the graph.
Recognizing that the vertex form equation is ...
f(x) = 3(x +1/5) -3 1/5
I might choose x-values that are -1/5 ± 1/2 to get y-values that are -3 1/5 + 3/4. And, x = -1/5 ± 1 ⇒ y = -3 1/5 +3.
