which equation has real zeros corresponding to the x-intercepts of the graph?

$ y = \log_3(x) - 1 $
$ y = 3^x - 3 $
$ y = -3^{(x-1)} + 3 $
$ y = \log_3(2x) - 2 $

Question

which equation has real zeros corresponding to the x-intercepts of the graph?

$ y = \log_3(x) - 1 $
$ y = 3^x - 3 $
$ y = -3^{(x-1)} + 3 $
$ y = \log_3(2x) - 2 $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Real Zeros and Intercepts", "Logarithmic Evaluation" ], "new_concepts": [], "current_concepts": [ "Real Zeros and Intercepts", "Logarithmic Evaluation", "Logarithmic Functions" ] } ## Identify the x-intercept from the graph Using the *Real Zeros and Intercepts* knowledge point $$ \text{The graph crosses the } x\text{-axis at } (3, 0). \text{ Thus, the } x\text{-intercept is } x = 3. $$ ## Evaluate the zeros of the candidate equations Using the *Logarithmic Evaluation* knowledge point $$ \begin{aligned} &\text{For } y = \log_3(x) - 1:\ &0 = \log_3(3) - 1 = 1 - 1 = 0 \quad (\text{Valid})\ \ &\text{For } y = 3^x - 3:\ &0 = 3^3 - 3 = 27 - 3 = 24 e 0\ \ &\text{For } y = -3^{(x-1)} + 3:\ &0 = -3^{(3-1)} + 3 = -9 + 3 = -6 e 0\ \ &\text{For } y = \log_3(2x) - 2:\ &0 = \log_3(6) - 2 e 0 \end{aligned} $$

(A) $y = \log_3(x) - 1$

(B) $y = 3^x - 3$

(C) $y = -3^{(x-1)} + 3$

(D) $y = \log_3(2x) - 2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Real Zeros and Intercepts" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the x-intercept from the graph

Evaluate the zeros of the candidate equations

Answer: